Heck, they could stop administrative fees (fees the university gets to itself) on state backed research funding at legacy schools and it would probably be very effective lol

The only private universities in California that are existentially dependent on research funding (unlike, say, LMU, which is basically just an undergrad teaching institution/networking mill) are CalTech, Stanford, and USC, and frankly I don't think anybody's arguing CalTech is doing anything but the most extreme meritocracy in their admissions.

Such a law very well could be challenged on it's constitutionality for how laser focused on USC it would be.