There's a reason you separate military and the police. One fights the enemies of the state. The other serves and protects the people. When the military becomes both, then the enemies of the state tend to become the people.
And their training reflects this. I've served in the army, but not in the US. Some units did get crowd control training, but it was very unusual and specific for their deployments (they were going to Kosovo). Preparing these units for crowd control required weeks of training. Crowd control is pretty much the opposite of modern warfare, with large number of troops marching shoulder to shoulder forming shield walls, ev…
Probably very specific, but I was in two non-US militaries and all combat corps were trained in Aid to the Civil Power, including public order, and were regularly refreshed.