> The US could have won militarily if they were willing to kill several hundred million people. It's probably best that they weren't.

Could they really? Would the nuclear-armed Soviet Union idly stand by and watch US commit nuclear holocaust against it's close neighbour? They wouldn't. Would US allies back them in a war that turned into genocide? Unlikely.

So no, they probably could not have done that because they would not risk escalation into WW3 where most allies abandon USA.