There is much talk about moving to free college in the US. What impact would that have? Some evidence of possible consequences is provided in The End of Free College in England: Implications for Quality, Enrolments, and Equity by Richard Murphy, Judith Scott-Clayton, and Gillian Wyness:
This paper examines the consequences of charging tuition fees on university quality, enrolments, and equity. To do so, we study the English higher education system which has, in just two decades, moved from a free college system to one in which tuition fees are among the highest in the world. Our findings suggest that England’s shift has resulted in increased funding per head, rising enrolments, and a narrowing of the participation gap between advantaged and disadvantaged students. In contrast to other systems with high tuition fees, the English system is distinct in that its income-contingent loan system keeps university free at the point of entry, and provides students with comparatively generous assistance for living expenses. We conclude that tuition fees, at least in the English case supported their goals of increasing quality, quantity, and equity in higher education.