Why exactly? I think the US ought to spend a few trillion on an actual space battleship - one that never comes down to the surface, just sits in orbit. There was a project regarding dropping telephone pole sized pieces of metal from space as an offensive weapon - put something like that on the space battleship and...

That is simply "Assured Destruction" with absolutely no mutual drawbacks or lingering consequences like radioactive wasteland. Just craters.

This is also something where the 1st country to achieve the "Space Battleship" could effectively prevent any other from also doing so...

In theory, Bezos or Musk could do it.

I don't understand why any country would bother with ground based military assets at this point.

That totally depends on the type of super villain organization we're discussing. Some are willing to watch the Earth burn making the colonization step unnecessary. Others think humans are the problem and again would be willing to skip that step.

It depends on the size of the asteroid and precision with which it can be aimed...