Their curriculum is not mandated. Their faculty need not be certified. A 180-day school year is not law. Or a five hour instructional day. Or any of the other endless mandates and restrictions on the public schools.
Every state owns institutions of higher education.
The answer can only be that it isn't necessary because higher education operates on the basis of choice. There are some fourteen million fulltime college and university students, and millions more of part-timers, yet not one of them is assigned to the school they attend, or required to remain there. Therefore, stifling government controls are not needed or used. Indeed it is. The Organization for Economic Cooperation and Development, the OECD, did a study of developed nations to determine the degree of local autonomy or flexibility possessed by the public schools.