Just adding a few thoughts on this proposal - and possible alternatives to it, from my own experience.
Here, not going to comment on the deleted articles. I'm not an admin so can't look at them to judge the average quality. But it seems very likely that nearly all of them are unsalvageable given the amount of nonsense that gets added to wikipedia every day and then deleted.
However, from my own experience I'm sure there must be at least a few that are good articles. It might be a tiny percentage. So whether it would be worth making them all in some way accessible though to rescue them is another matter. I don't know the answer there. It might be that you'd end up with so many articles that sifting through them to find the good content is totally impractical.
If it's not possible to do that - what about some easier way to pick out good articles during the deletion process itself?
Could there be some way that wikipedians can nominated any good already deleted articles (if they are admins) or articles about to be deleted (for everyone else) as "good articles but not for wikipedia"?
And then could we then have some place to put them, similar to the drafts, but labelled as "not for wikipedia" - of course not findable in wikipedia searches or in google, but findable in specialized searches where you look through the rejects for interesting material?
So anyway - before getting to a detailed suggestion, first a bit more about why I think there must be quite a few good articles amongst all the rubbish deleted articles.
PROPOSED DELETION ARTICLES
I used to patrol the "prod" articles - and when I was doing that a while back, some got tagged for immediate deletion that didn't deserve it. This is a template that anyone can add to an article, and - if nothing is done, the article gets deleted.
When an article is "prodded" then a big rather scary notice appears at the head of the page. If you read it carefully you find that anyone can remove the notice, even the author of the article themselves. But newbies often don't realize that.
It's a way of making it easy to delete rubbish articles without having to go through a discussion. So it has its place. But it does sometimes lead to good articles being deleted. I rescued a few of them while I was doing the patrolling. Often all that was needed was a bit of a google search and then adding citations to the article that fit the wikipedia criteria. I'm sure that there must be a few good articles that slipped through the net in the early days though nowadays there are so many people patrolling them that it probably doesn't happen so much nowadays (and I gave up patrolling them myself as I seldom found articles that needed to be rescued any more).
Anyway - though less likely nowadays to find a good wikipedia article about to be deleted for lack of citations or some such - there could well be articles that would be good elsewhere, but have just been submitted to the wrong place.
ARTICLES FOR DELETION AND ARTICLE RESCUE SQUADRON
Apart from that you have the articles for deletion. There's an Wikipedia:Article Rescue Squadron which patrols these to try to fix issues so that good articles don't get deleted just because there are issues with the sources etc that could be fixed easily.
So again - that that squadron exists at all shows that occasionally articles can get deleted that could have been rescued and used in wikipedia with a bit more care and attention.
GOOD ARTICLES NOT SUITABLE FOR WIKIPEDIA
Then, you get articles that are good articles in themselves, but in one way or another are considered not suitable for wikipedia.
There's nothing wrong with it as an article, and astrobiology friends have said it's a good article and useful survey of the field - but it was judged to be too detailed for wikipedia - and also - too much reliance on the original sources instead of secondary material such as published overviews of the entire field.
In the end I posted that one to my blog, but it clearly belongs in a wiki so it can be updated easily by experts, at least once every few years - and I'm still looking for a good home for it :).
So there may well be many articles like that also. Good articles in their own right, but not suitable for wikipedia.
Another article of mine was this one, which I originally wrote for wikipedia, but again they didn't want it, because it relied too much on the original source material and also presented ideas that were considered to be too fringe to be included in wikipedia in the medicine topic area (which understandably has stricter policies on fringe material than other subject areas).
So again, that didn't mean at all that it was a bad article in itself. Just that it didn't fit the criteria. So I just reused my wikipedia draft article as a science blog post instead.
I GOT STARTED ON SCIENCE BLOGGING WITH A WIKIPEDIA REJECT ARTICLE :).
And indeed several years ago I wrote an article on Mars Sample Return which I thought was good but it was deleted with an article for deletion discussion. That got me started science blogging :).
The solution I found was to post them to my Science20 blog or to Quora instead.
This is one of the places where I can write things that are not acceptable in Wikipedia for one reason or another.
MANY POTENTIAL OUTLETS FOR WIKIPEDIA REJECTS
So - with many outlets now for articles like that - then there are places where you could put rescued deleted articles from wikipedia, and there may well be quite a few of those, amongst the probably thousands of articles that are of no interest - I think there are probably at least a few very interesting deleted articles that are good articles in themselves but for one reason or another either don't fit in with policy.
Or indeed might be that sometimes they are unfairly deleted, the system is only as good as the people who assess the articles and if an article is in a specialist topic area it may only get the attention of a few people who may not be expert enough to assess it - that's the downside of the methods used to assess the articles, which also has many upsides.
Anyway - it doesn't seem too likely they will give access to deleted articles except to admins. And it would probably be a long job searching them for good material unless you happen to know a particular deleted article you want to rescue.
But - I wonder if there is any value in a "wikipedia rejects" user space - or as a separate wiki - with some easy and automatic way to move good but unsuitable articles to it?
DRAFTS FOR NEW ARTICLES
One thing you can do is to browse the drafts for new articles. May be interesting material there.
The way the system works - these are not deleted from view, they are just not accepted for the main space. Don't turn up in searches in wikipedia, excluded from google etc. There are many of them, and you might be able to "rescue" old drafts for wikipedia, or use them elsewhere (within the limits of the wikipedia contents licenses).
As a new user, or if not too sure of the reception for your article - it's probably a good idea to do it as a user space draft first. Then if the reviewers don't like it - it doesn't get deleted and you don't get a stressful and sometimes acrimonious article for deletion discussion. Instead you get polite and helpful comments on your article telling you how it can be improved for wikipedia - and it just remains in the draft space and you can continue to work on it.
So - if the article was created as a draft - then - you don't need to look through deleted articles, because they never get to the main space in the first space. So they are still available to read by anyone.
Sometimes though, an article passes review as a draft - and later gets deleted. That's what happened to my Morgellons article - I wrote it as a draft, then it was accepted, and then it got deleted in the mainspace. And then I was requested to delete all drafts for the article from my user space, which I did. Not sure if they really had the right to ask me to do that, but I had no wish to be contentious there :). By then I'd already written it up and posted it to my science blog and had no need for the user space drafts any more.
FOR ARTICLE WRITERS - IF YOUR ARTICLE IS REJECTED - DOESN'T MEAN IT IS A BAD ARTICLE - JUST NOT FOR WIKIPEDIA
And as for article writers, I think it is important to realize that just because your article has been rejected from Wikipedia or deleted there - it doesn't mean it is a bad article in any intrinsic way. Just means it was not judged suitable for wikipedia. Which could be for many reasons. My wikipedia rejects have inspired some of my best science blog posts :).
DETAILED SUGGESTION
So to flesh this out as a somewhat more detailed suggestion. Whenever someone deletes an article in wikipedia - or rejects a draft for the main space - at present it is up to the author of the article to make a backup. And often they are expected to delete any backup from their user space after a short period of time if it is judged not suitable for wikipedia.
So - it's rare that any trace is left of a deleted article, no matter how good it is, unless the author actively makes a copy somewhere else. And especially because they use the wikipedia templates and are not very portable even to other wikis, chances are that any backup they make is not as easy to edit and update. Even if they backup the wiki text, they can't actually use it. And may only exist on their own local machine.
And many authors will be so discouraged by the deletion of the article that they will just give up on it, not copy it anywhere else, and there is a chance they may also give up on wikipedia too.
Instead I suggest that whenever admins delete an article in wikipedia they have a multiple choice option to:
Delete it right away. You would do this for articles that breach copyright, or are just vandalism or nonsense, or are so badly written it's hard to tell what the subject is and such like, and looks as if the author has spent only a few minutes of thought on it, just rambling "of the moment" writing - or that are breaches of privacy, or in one way or another are obviously things that shouldn't be made available for public view.
Move it to the draft space of wikipedia - if it is an article that could possibly be rescued by another author as a wikipedia article, or could be a source of material for wikipedia articles
Move it to a "Wikipedia rejects" wiki - which could be further categorized into categories such as "Original Research", "Fringe", "Only of local interest" (all those articles about e.g. detailed history of a particular school, which may be of great interest to a few people who have attended that school, or taught at it, or worked for it, but don't belong in wikipedia) and so on. This wiki would have all the same templates etc as Wikipedia itself - maybe auto backup the templates from wikipedia - so that the articles display in the same way as on wikipedia and are easy to edit.
And - that would be done automatically - multiple choice - that when you delete an article you have to make a decision about which to do.
The wikipedia rejects wiki would be excluded from search engines. So it's not an alternative place to publish your article on the web it is literally just an archive, like the history pages in wikipedia for instance.
So you can only search it from within the wiki - so that you don't get search results showing the rejected articles alongside the ordinary wikipedia articles. (Or maybe a custom google search - the only drawback about only searching it within the wiki is that often google searches work better than the wikipedia internal searches - so if there was some way to let google search it, but only if the search was restricted to the rejects wiki - that would be ideal).
In the Prod template for articles for immediate deletion, then the decision is made by whoever adds the template - would have an extra parameter to say which category it should be deleted to. So then the admin just does whatever is suggested in the template unless it is obvious that it belongs somewhere else.
For AfD discussions, then participants would be encouraged, when they say that it should be deleted, to say which of those categories it should be deleted to. And closing admin, as usual, makes final decision.
For draft article reviews, then the reviewers would have the option to suggest that it be moved to the rejects wiki if they think that it is unlikely to ever be suitable for wikipedia. But in that case just as a suggestion, they don't automatically move it - because the author of the draft might think they can rescue it as a wikipedia article.
It's just a thought. And one I had just now, while reading this question. So for discussion, maybe there are flaws in it.
But if it worked, it might save a lot of duplicated work, and deleting things that people have sometimes put a lot of work into, sometimes months, sometimes even a year of work or more before someone notices that their article doesn't seem to be suitable for wikipedia and it gets deleted.
And it would also be a way to show that you respect the amount of work they put into the article, and their good faith and generosity putting so much time into trying to improve wikipedia - but just say that it is not for wikipedia.
And they may then feel more favourably inclined towards wikipedia, and not have the same feeling of rejection and hopelessness and helplessness you can get if your article you have worked on for so long gets deleted by others beyond your control - and so then they may be more likely to return to it later and work on other articles that are more suitable for wikipedia, once they get this feedback about what is and is not acceptable. But with all their work - the acceptable articles and the wikipedia rejects alike - treated with a higher level of respect than it is now.