lets not speculate, but instead use freely available data.
The most innovative countries in the world, (the Scandinavian states) have free tertiary education.
The country with the highest prison population (USA) has the most expensive tertiary education.
QED
It all depends on what you think we are here for, to compete to polarise wealth or to cooperate for a universal improvement.
If you want a nation of a minority uber rich elite and a criminal underclass then make the tools for improvement expensive and unobtainable. If you want a free thinking nation of innovators then educate the hell out of everyone.
Remember you as a nation can either pay for prisons or fund free education it's a political decision that your politicians make. Ask yourself why they make the decisions they make.