It's actually unlikely, as state licensing boards have the power to legislate who receives a license and for what reason as they please. Same goes for prescribe numbers- they could just tie prescribing rights to Medicare enrollment, in the same backdoor manner they force seniors to accept Medicare or lose their Social Security benefits.
As to mandating your patients, well, they could require that X% of your panel be government insurance for licensure. You can pick who, but they still have to be on your panel.