Instead of going right for the Product Manger role, people should aim for some sort of delivery internship. And from there a Business Analyst role, Software Engineering role, UX Designer role, Quality Assurance Engineering role... anything hands-on. This sets them up to be good at Product Management -- better than the kids who come straight out of school anyway.
There's a good amount of "inflation of self-worth" (for lack of a better word) around people coming out of college right now. It's true that college costs a lot, but virtually everyone has a degree. AND we all know that there's massive grade inflation going on -- so it's hard to take a college degree seriously. Also hard not to have one... not an ideal situation, to be sure. (There's a lot of role inflation too... people now are "senior" with a year or two experience? Come on.)
Anyway, requirements are inflated to screen people with 0 experience out. If you have done well for a few years at a staff role, nobody is going to care that you don't specifically have N years as a product manager. But it's a HUGE risk taking someone out of college and giving them a leadership position. Better for them, and the company that hires them, if they spend a little time in the trenches.