Fine with it being universal, but the draft didn't stop us from either Korea or Vietnam so why would it stop the next war? Heck, Vietnam may be the conflict where we had the least strategic interests or geopolitical considerations of any major conflict we've been in.
Because if you were wealthy or important you didn't have to go. If you went to college or did other things that better-off people did you were exempted. The elites never had any skin in the game for either one of those wars.
If the last 20 or so years of American military history haven't taught us the lesson, the draft never will. Whether it's to "stop terrorism" (Afghanistan), remove dictatorial threats (Iraq), or "standing up for human rights" (Somalia or anywhere in Africa for that matter) none of them have really been worth the price.
I'd be hesitant to compare Somalia, etc, to Afghanistan or Iraq. Our involvement in those other conflicts was tiny in comparison. Regardless, related to my point above, the people in charge were never worried about being personally affected. If their son or daughter was in the military as well I wonder if they would have second thoughts.