If they are trying to prevent having to pay even bigger bills later when the kids get deathly sick from getting a preventable disease then, from a business standpoint, yes they should. But from a parental control standpoint no they shouldn't.
No one is pinning down medicaid kids and vaccinating them. Its more of a "follow the program or leave the program." Medicaid coverage is optional!
I have a scholarship that requires me to get a B or better in the classes that I use to pay for it (its an accounting scholarship, so it covers accounting classes only in their books) and I have to submit transcripts every semester. B or better and its renewed, C or below and I owe them the ~1k for the class within 30 days or it goes to collections. Is it fair? YES. Its free money! You can make rules for the free money you hand out.