For example Columbia University, Harvard, Dartmouth have the plan of giving free tuition to students who’s parents make less than 60,000 dollars a year.

How much financial aid a university awards its students depends on the tuition costs, the family’s estimated contribution, and the money the university has available. The schools that you listed have high tuition rates because they are private universities, that household’s under $60,000 would not be able to afford..that is why they give free tuition to the students that are academically excellent, but not rich. When tutition is higher, you will find more financial aid, but that does not necessarily mean that it will be cheaper overall.