It takes 1-3 years of facility based training in order to qualify as an ATC for a specific tower. A military enlistment is only 4 years. CCTs would end up doing their entire enlistment at one facility leaving no time to train as a CCT. You'd have to hire another person who's job is 100% CCT, at which point, why not just hire an ATC?
Military enlistments vary from shorter than longer to 4 years.
ATCs regularly go TDY to support other locations.
You’re conflating ATC training with a location