Arguably a high minimum wage would mean no one would want rubbish burgers any more, so perhaps burger flippers would have to retrain as chefs. That wouldn't be such a bad thing.
You can say the same thing about any job. I program. It's a terrible, worthless, respectless job. And yet, they're paid more.
Ha, they'd give up on years of income and pay tuition for that? Nope, I think a lot of people either wouldn't care enough, or just wouldn't be able to afford the opportunity cost. For many of the people whom a 70k minimum wage would affect, college is a financial investment, not a route to lack of tedium as an accountant or whatever.