Cost is relative. $100 is a lot of money to a low income individual, but not a lot of money to the CEO of a tech company. "Free" is the one cost that is equal to all. Socio-economic disparities are global, and for some individuals the cost of public tertiary education is a burden that is not possible to overcome. Through government funded tertiary education, the economic barrier to entry is substantially reduced. This benefits society as a whole, allowing for more civic engagement from college-educated individuals. An increase in the amount of college-educated citizens would also benefit the economy, allowing society to pull from a larger pool of problem-solvers to innovate, thereby creating jobs. Though the cost to be borne by the government is high, there is a significant enough return to justify it. Free tertiary education is also more equitable in this respect. It's an education system that values what someone knows over whether or not they can afford tuition.
It is possible to overcome economic barriers to tertiary education without making tertiary education free to all. Some governments offer loans, grants, and even scholarships. Financial aid is even offered in some countries, though by itself it may not be enough to make tertiary education affordable. However, when combined with any of the aforementioned forms of financial aid, the cost of tertiary education can be made affordable to all.
[P1] It benefits society to have more people attending tertiary school. [P2] Societal inequalities makes it difficult for some people to attend tertiary school if there are associated costs. [P3] Tertiary school should be completely free for all.
Rejecting the premises
[Rejecting P2] While cost may be relative, there are ways to adjust for this without making cost nonexistent.