But there are two big problems with a USSAC Empire -
1) Of countries most likely to stab each other in the back, the US, Russia and China top the list.
2) Both the US and Russia/USSR more or less failed at containing Afghanistan. If they can't contain a forsaken country like that, I don't see what hope they have of conquering the entire planet, even in the highly unlikely event that they pooled their resources. They could probably get away with pushing Europe around, but I think the rest of the planet would give them a lot of trouble.