I think that if US breaks up there wouldn’t be a single unified military anymore. Plenty of states hate each other, so it’s far more likely that there would be a bunch of states pursuing their own interests as opposed to a single nation projecting unified power globally. Collapse of US would certainly lead to the end of global hegemony as well.

We can also look at what happened after USSR collapsed, and that was a far more civilized process than what will happen when US collapses.