The amount of money, infrastructure, skilled teaching staff it takes to establish a university presents massive barriers to entering the marketplace. Assuming you're comfortable marketizing the education of the next generations, it would be done by large private companies with considerable market influence. It will become less about learning and more about a graduates career prospects, with companies producing conformists who will work in the corporate machine. Standardising the mind to fit the requirements of a corporation will reduce the risks of people thinking outside the box, and that people should be spoon fed the "safe" ideas rather than critically questioning the society, it's knowledge and looking for opportunities for it to develop?
Are you seriously comfortable with the individuals freedom of thought be determined by the highest bidder in an education market? If a corporation can indoctorinate young people for profit, that would prepare the infrastructure for government to do it by making overt political partisanship in education 'normal'. this is a gross betrayal of the principles of libertarianism and the principles on which America was founded on as it curtail a democratic society's ability to have an informed citizenry.