You really, honestly think that the children of the powerful elite of either party would be included in a draft, and not just get put in a stateside "champagne unit", if they were drafted at all?
You're very naive, if so.
A draft just sucks up people from the lower classes who didn't want to enlist, and sends them over to be a burden on the people who did sign up and are dedicated to their service. The wealthy and powerful get their kids out of it. That's how it's always been, that's how it always will be.