I fear that creates an incentive to game the system. "This person is dislexic so we get the dislexic bonus", but they're really not, but parents work to get their child labeled as such so they can get into the top schools, and the top schools take this "not really dislexic" child, which they can interview or test to ensure they're perfectly capable students.

I think this would actually be a case where the stick works better. A school can't reject anybody. And if a student leaves your school with a complaint about service you are severely punished. Maybe funding cut by a percentage of the size of the student body per complaint.