Scholarships and financial aid help, but they can only go so far in lessening the cost of higher education. There should be a cap on the tuition universities can charge, and it should be something reasonable, not an outlandishly exorbitant amount. Something that a decent percentage of students can actually afford.
No matter how many "free" education options are made available, there is always going to be demand for additional education by those who can afford it. There's no reason the market should be forbidden from supplying that demand. Doing so would decrease both the availability and value of higher education in a misguided attempt to level the playing field.