I don't believe that it affected his care. There were a fixed number of hospitals, inpatient rehabs, and visiting nurse associations, and they all took his plan. And I can't possibly see their behavior being different for a different payer - the incompetence was intrinsic to their deliberate bureaucracies. The only way to rise above would have been to find providers that didn't take "insurance" at all, such that the actual customer was the patient rather than another bureaucracy.
The Medicare rules were limiting by fixing the amount of rehab sessions he got per week. The length of his care would have been limited too (discharge rules), but I advocated to extend him within the system. But any bureaucracy is going to be similar, and thus the only way to fix that would be neutering the whole "insurance" cartel and forcing the industry into radical price transparency. Which is basically the line I was straddling with the private pay helpers.
What Medicare really helped with is making his copays sane and giving me solid footing to push back on billing fraud. For instance, one equipment supplier sent me a bill for 50% more than it should have been, and then shamelessly stood by their story on the phone ("you owe us this amount, so you need to pay"). I presume they successfully defraud many people that way.