Shared military is probably the single strongest reason US states could never leave the Union. It comes up every single time Texas or California talk about secession. Some of our largest military operations are in those states, they would never be allowed to leave. Once you have nationalized military you have soldiers with no allegiance to your own state in all your bases and your own soldiers are spread thin among all the other states with no way for you to recall them without appeasing the current head of the military who is also always more loyal to the union (or the military or themselves) than your state.