Historically, large publics have not done this (I have heard of some privates acting shady in this regard, however). If you think about it, it makes sense: Not only would it be unfair to students but large publics have more levers to pull to make numbers work: they could take in more full-pay transfers (they typically take in a good number already) or just admit more and cram more students in to the same number of classes. And the cost savings may not be that big if students who lose their scholarship transfer away.
IMO, I don’t think this should be a high-level worry compared to many other issues to worry about.