10 billion dollars isn't enough to fix that; but it's enough to put boots on the moon, and give people something to look up to and say "we did that".
Sure they could. As a counter-proposal, I say we buy ten billion dollars of garbage and put it in a big pile in the middle of the country and set it on fire, so everyone can literally look up to the President Donald J. Trump Literal Flaming Mountain of Garbage and say "we did that." They can go see it, too, and roast Trump steaks over it and breathe in its heady fumes. Can't do that with a Moon base.
It'd even be a more accurate statement than the space equivalent. After all, the vast majority of Americans have nothing whatsoever to do with space exploration and happily say "we" went to the Moon anyway with perhaps a twinge of guilt in their more introspective moments -- but with my plan, every time they take out the trash they can say with pride that we, all of us, built the President Donald J. Trump Literal Flaming Mountain of Garbage.
Now, to be sure, the garbage pile doesn't help anyone but a very few, but neither does a Moon base, at least not without a more defined purpose than anyone's provided thus far; it might make some rich people richer selling refined regolith or something, but the average American does not tangibly benefit from either one. We can of course pontificate about how it's our future as a species and an expression of qualities inherent to the American spirit -- but, truth be told, a staggeringly expensive self-created ecological catastrophe with no real point is probably a more honest self-portrait.