If the miltary can’t trust every member who has completed basic training there is a problem.
Note that I said At minimum, sergeants(E-5) and above should be allowed. As a first step, have them be armed, and see what happens. Then, bring it down to corporals.
In civilian life, we generally don't allow 18 years olds to have CCW. It's 21 and above. By the time somebody has gotten to be a sergeant, he's been in the military for 4 years, and is over 21.