You can't just send EVERYONE to Berkeley/SUNY/UW. "Prestigious" is inherently anti-universal-access. The only solution is to crush the power of these prestigious universities.
I think you're missing the point. The issue isn't that every student can't go to Berkeley, it's that identically qualified students students can be charged 500% more for the opportunity purely because of geography. I suspect this disparity might actually be weakening the "prestigious" nature of many schools given there is now a monetary incentive to accept unqualified students if they are out of state (or even out of country for even more fees).