this would work. but it would be horrendously regressive. Today kids with wealthy parents have great advatage. In your future, it would be overwhelming! overnight college rates would plument, and again the college degree would be a golden ticket... for the kids whose parents had the gold.
now if you taxed the heck out of all tuition beyond $X thousand per year, and used all that money to fund loans, such that at least Y% of the population was going to college, then you could achieve the same thing you are aiming at.
but that aint ever happening!
but what you propose would evicerate the chances for those who below the median.