Try booking a doctor's appointment in the US on a Medicare plan vs. under private insurance. You'll find that the former gets pushed out weeks and months, whilst the latter finds availability within days.
Doctors love Medicare. It pays them nearly instantly, steady stream of clients, and known fixed rates commensurate with most private negotiated rates.
Medicaid is the one that has much stricter benefit rules and tighter price guidelines.
To which I would say that is wrong because the person working at the MCO reviewing the claim would not be evaluating the expensive procedure based on if the insured has Medicare or Medicaid, they will approve or deny it the same if they deem it medically unnecessary.
I agree that healthcare providers get paid differently based on the patient’s coverage, and that would influence the priority they give the patient. In fact, I would say the whole point of the convoluted MCO system (versus a simple taxpayer funded system like UK) is to give the government plausible deniability for segmenting the population into various groups of people getting different quality levels of healthcare.