You can understand why this would be an advantage to the government - but why would the extra terrestrials do this? That's the big problem with this idea.
Also - remember that it's extremely unlikely that ETs would arrive here just as we reach technology. And if they did, surely they evolved at least a few million years ago (would be almost absurdly unlikely for them to evolve to a similar stage as us at almost exactly the same moment in geological time).
So - if they are here, they would have technology from thousands of years into our future. So their spacecraft wouldn't crash, not with such a simple mission as a landing on a planet. And - surely they wouldn't send themselves down to the surface either - they would send avatars, robots to come here first.
And their technology would not be just a decade or two in advance, but thousands of years in advance. I don't think there is the slightest chance that the US is in possession of technology that is a thousand years ahead of everyone else, or any other government. They would be sure to use it for civilian means, write off their debts by generating energy, or making things etc using simple machines that will be invented a few centuries into the future.
And as for contact in the past - why didn't past civilizations learn basic maths such as ratios, equations with negative numbers in them, the decimal point, zero, logarithms, etc etc.
So, no, I don't think we are in contact with ETs or have been in the past. If there are any there, they surely have a strict no interference policy. Or perhaps they just are not here yet. Or their robots could be, but so unobtrusive we'll never find them.
It's also obvious that they haven't colonized the galaxy, at least not in an exponential fashion. If they had, again would be astonishing if they evolved just now, so they would surely have done so a few million years ago already. So would already be here. Indeed the galaxy would be overflowing with them and probably have constant warfare and boom and bust cycles.
I think therefore that if there are ETs in our galaxy, then either they just don't go in for colonizing at all - perhaps because they see the many things that could go wrong if they filled the galaxy with their kind plus all the inventions, and other beings and replicating machines they could produce - or else - if they do - they do so in a way that is unobtrusive and has minimal effect on the galaxy.
It could also be that there are very few ETs, compared to the size of the galaxy, and that some of them are great travelers, long lived, think nothing of crossing the galaxy several times at sub light speed, and one of them is due to visit Earth some time in the next few thousand years.
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