I don't think we could ever start the draft again because of the social problems that it would raise. When we last had a draft, society largely acknowledged that homosexuality was wrong. Men who had this problem and were called to serve generally fought it and tried to live as heterosexuals during their time in the service. Today, they would try to continue being openly and actively homosexual. Some would try to use their homosexuality to avoid service while others would try to use it to force the services to allow homosexuals to serve openly.
We would have similar problems with how to handle women. We once saw men and women as people would be someday be partners in a traditional marriage. The man being drafted to defend his country was also defending the woman who would someday be his wife even if he didn't know her yet. The time during which he served was not time during which she would be at home building an advantage that she could use to beat him in the job market when he returned. Likewise, the educational benefits that he received for his service were not seen as opportunities denied to her because she would benefit from his opportunities when they married. Today, men and woman are more adversaries and less partners. Being drafted would have different effects in different situations, but it wouldn't be "equal." Our society's preoccupation with "equality" would make handling the situation difficult.
I don't think we should use the draft as a form of social engineering. I've heard people on both the left and the right suggesting that the draft would be a wonderful way to force their values on society. I think using it for this purpose is a big mistake. I write about all of this in much more detail at Peacetime Draft, Bad Idea. I realize that we are not exactly discussing a peacetime draft in this thread, but many of the problems are the same.
WFTR
Bill