I believe this is all about putting pressure on universities by whatever means are available. It's the threat that matters with the hope that universities will cave or negotiate about whatever the Administration wants. The details don't really matter much...
The universities have proven themselves to be weak, which leaves a wide opening for the next Democratic administration. They can tell universities to toss out the right wing garbage and force them to teach the courses the right wing hates. They have given in once, now they have to give in always.