I agree, though it should be noted that this is how many private property claims arise. Certainly intellectual property is state-created, but one could argue that even the value of traditional real property has everything to do with the regulatory conditions under which it subsists. Change the regulatory conditions and you have a potential takings claim.
You have a property interest in the use of your own property; you don't have a property interest in preventing other people from using their property.
I've got several friends and one family member in various stages of med school and post med school, and I've never heard anything about restrictions beyond the fact that most people decide being "pre-med" isn't for them after they take genetics and organic chemistry
For intangible property? Absolutely, you have an interest in preventing people from using their stuff (they can't use their guitar to play my song, for instance).
If they paid for their medallions, and the market at the time valued those medallions as fee simple that would always be held by the owner, there's gotta be a good takings arguement there.