First, the reason it's broken is because, aside from lip-service, most citizens and politicians don't give a shit about vets. Why? Because most of them never served, never wanted to serve and don't know anyone that served. One main problem with ending the draft is both ending that commonality of military service and that military service is becoming more of a family thing. Children of service personnel join the service themselves and far fewer sign up out of the blue. Aside from the wave of patriotism after 9/11, military service has become increasingly cloistered and separate from mainstream Americans. That could turn into a bad thing in another 30-50 years. .
Second, inefficiency is part and parcel of bureaucracies. Improvements can be made but the larger the agency the more inefficient it becomes.