The military on the show is pretty much retired people that the aliens didn't kill, who came out of retirement.
The amount of people left is next to none. If I lived in that world I wouldn't call what is left the USA.
Neither would I, but that's easy for both of us to say not being in that situation and never having lived through what these people have.
I look at it this way: There are some people - shocking, but true - who think that it's important to have a United States in the world, for the idea of it if not for the population or industry. For them, the reality of it containing only a handful of people in one town is immaterial. A United States is necessary and desired, and it might be something nice to have if the aliens ever get kicked off the planet later, so they recreated it. You disagree. Fine. If the day comes when we all get our asses handed to us by Klingons and you survive and find yourself in a position of leadership, you can reshape civilization in any way you like.
It won't matter, because I, Imperator of Colbournetopia, will be along presently with my legions to enslave you and hear the lamentation of your women.