As for the roads example, which would go to my second point if I understand you correctly, I think the analogy is limited: roads aren't gate-kept by admissions committees for certain intangible criteria for who can ride on them, with an artificial limit on how many cars overall, while they receive federal funding. If that was happening, then you'd have a similar situation to what universities are doing.

It's not meant as an analogy for this case, so don't worry about it too much. My only point in bringing it up is an example of evidence for prior governments being more than willing to use funding as a lever to influence the policy of institutions they are not directly responsible for. I don't believe it was to be 1:1 to make that point, as indeed it is not.