Well I didn't serve either, but I agree with your assessment - the military makes a good person better.
The last thing the military wants is a draft. The quality of the fighting force would drop dramatically. You won't find anyone in any of the services that is in a position of manning that service nor anyone in the service leadership, military or civilian, who would support a draft. The last thing they want are people who are not committed and don't want to be there.
Food for thought: some sort of national service might be OK here as well, if it results in responsible adults who know how to behave like adults.