Absolutely. A draft would also force Americans of all backgrounds to interact with each other in an environment that builds cohesion. It would also give even the most powerful of Americans skin in the game when it comes to starting wars.
Every American presidential election has a side show about the candidates military record and a meaningful number appear to have dodged their service - current president included.
I think we should just accept that the hypocritical institution is dead after Vietnam and stop trying to use it for power fantasies over society or advocacy - its only function is to snatch defeat from the jaws of victory as it makes reasonable ideas grossly unreasonable.