Every doctor I see is a Medicaid provider. Yes, there are doctor who don't accept it, but it's not hard where I'm from to find a doctor who does (perhaps we have an oversupply of doctors?).

"Medicaid provider" and "Medicaid provider taking new patients" are not the same thing. They'll usually set a maximum number of Medicaid patients for the practice, and there'll be a long waiting list for that.