You have (almost?) entirely public institutions chartered under state constitutions colluding to attempt to create a self-beneficial and exclusionary for-profit system within the confines of a tax-exempt education system, all without any Federal oversight and under the auspices of "it's education".
If they want to play the "it's education" card, then education is subject to regulation under Federal aid laws - cue the Federal government. If they don't, which is where I think this will land, then spin the whole thing into its own enterprise unrelated to education, recognizing that all profits should be fully taxable, and seek to obtain an anti-trust exemption.