The ideas to terraform Mars are temporary. It would lose its atmosphere again over a period of perhaps a few million years or longer. This is just a guess - the Maven spacecraft will find out more and is finding out more. MAVEN Will Look at Key Player in Mars Atmosphere Loss
That's one of the many reasons why I think that we shouldn't terraform it, because if we do we have responsibility for those future beings on a planet which is gradually losing its atmosphere because of what we did.
After all you are already thinking in terms of people living there a thousand years from now. So why not also think about people who will live there a million, or ten million, or a hundred million years from now? They are people just like us. Or - intelligent creatures anyway. Maybe they have lost their technology. Or just haven't been able to maintain the industrial base for a long term industrial space capable civilization. And their world is dying because we were impatient and started on terraforming Mars a million years before their time and made some mistake in how we did it because we did it before we knew how to do it properly.
We are technologically young as a species, just had space technology for less than a century. And we can't even manage the atmosphere and climate of the Earth.
How can we possibly think we are mature enough to do planetary ecoengineering? Especially with a project that would need to be sustained for a thousand years just to get to the point where you have trees but no animals or birds and humans still need aqualung air breathers?
How many space projects have humans managed to sustain for as long as, say, 50 years? And now planning to start on one that requires billions of dollars spent every year for a thousand years?
And there are so many ways it could go wrong. And - e.g. they say there's enough water to cover it to a depth of some meters - what that forgets is that it already has only a tiny ice cap and a terraformed world at distance of Mars would still have ice caps - larger than the ones it already has - even if it had oceans. And its equatorial regions are dry probably for kilometers depth - what happens when you pour a few tens of meters thickness of water onto a desert as dry as the Sahara?
And as well - well if it was true that through just tiny changes such as greenhouse gases and mirrors, humans can release enough CO2 for a dense atmosphere in as short a timescale as 1000 years - well that means that Mars is so sensitive to tiny changes, that some other tiny change, something we didn't plan, could as easily cause it to lose its atmosphere in a thousand years. Not escape into space. But freeze out (e.g. because of more clouds than expected) or get caught up in unexpected chemical reactions or whatever.
But by far the most unpredictable part of it all - we don't know how life would adapt and evolve, if introduced to Mars. Or indeed what life is there already and if so how it would react if we tried to terraform Mars.
The problem there is, once you introduce life to Mars, whatever it is, you can't ever remove it again. So what is it going to do to the planet?
We could end up with a Mars with an ecosystem of life that works just fine, but is totally inhospitable to humans, for instance.
E.g. produces huge amounts of hydrogen sulfide, or methane, which are poisonous to humans. Or has organisms that are allergens for humans or toxic to us, as the main microbe in the ecosystem. Just to give a couple of examples. Many other ways it could go wrong because we don't have the experience to know how to do it.
I'm not sure this is a project even for the 23rd century. Maybe start on it some time around the year 3000 if we have learnt enough by then :). But by then we might also have learnt enough to realize it's better not to terraform Mars.
And as for the idea we need to become a multi-planet species. Yes about 500 million years from now we may need to be. Because then the sun would get so hot that the Earth would be uninhabitable. Then might be the time when we need to terraform Mars, if we ever need it. About as far into the future as the time it took for humans to evolve from the first "modern" microscopic multicellular creatures. Probably thousands of technological civilizations and maybe dozens, or hundreds of new intelligent species into the future.
By then - or some time in between then and now, good chance that someone or other reaches the level of understanding and maturity to be able to terraform it responsibly - if that is indeed the best thing to do.
But not right now, what's the point in terraforming a planet using methods that can never make it as habitable as Earth and will soon leave it uninhabitable again at least on geological timescales? Since the disasters that they want us to be multi-planetary for also happen on geological timescales?