US drafts work from the bottom up. Because as you go higher up (e.g. people in college, then blue collars, then white collars, then leadership...) those people are increasingly indispensable to the war effort. In Vietnam, they made universities give them lists of the students that were doing badly to draft first, once they ran out of people not going to college.

And if I had children, I would definitely consider relocating them abroad as an option, depending on whether they personally agreed with the war and other factors.

In short, as you go up that hierarchy, people are increasingly politically active, yet are increasingly isolated from the draft.

So, if you wanted this solution to work (and I contend it's a very poor solution to the problem anyway), there are some serious obstacles.