I assume you're talking about public colleges and universities. I also assume you're not also proposing that room and board be free as well. As you may know, public higher education was largely free until the early sixties, when modest fees were introduced. Over the last fifty years the cost of higher education has increased quite beyond the rate of inflation, and fees have increased as well. Why? The reasons are oft-described, but not--at this time--easy to remedy:
1. The enormous increase in the size and remuneration of administrators and their supporting staff. A great deal of this comes from the need to comply with the ever-increasing burden of government regulations, mandates and threats, but much of it also comes from the assumed necessity to minister to the ever-enlarging panoply of perceived student needs. An office of Gender Equality was unimaginable in 1955, as were counselors to help students through the supposed rigors of campus life.
2. The enormous increase in the size and remuneration (at the professorial level) of faculty. At most schools, the number of hours that an individual professor teaches has declined considerably since the 60's at the same time as salaries have increased.
3. The proliferation of courses that are offered primarily to please a pressure group or satisfy a current fashion (various race-based studies programs, gender studies, film studies). They cost real money to teach and administer, and they take up space, leading to the need for more space, meaning new buildings.
4. A significant number of new programs in advanced science and engineering, programs that require not simply new buildings but sophisticated and ever-changing equipment within those buildings.
5. Competition for students. Lavish student unions, sports facilities, gymnasiums, dormitories. The list could go on. A climbing wall was as unimaginable as an office of Gender Equality in 1955.
6. Undisciplined faculty and students. Unless a student has a demanding part-time job, a four-year degree shouldn't take five years. Part lack of direction, part laziness and--too often--paucity of academic offerings because the faculty has decided it has better things to do than teach.
7. The ubiquity of easy student loans. More money = desire to find ways to spend more money
8. Finally, the tendency of organizations to expand, to seek more power and riches unless checked. Take a look at the expansion of nation-states, or the EU.
Were higher public education to revert back to its prior state when it was free, I'd be happy to support the idea that it be free again. Until then, I look to places like Hillsdale and to provide models for responsible higher education. Not the only models, but admirable ones.
https://www.hillsdale.edu/
https://www.berea.edu/