Some years ago, I met a doctor on vacation - bit of an ass, but whatever
Last year, I found out he’d gone to prison for “performing procedures” that he was mot present for, including some whilst he was on the beach in Fiji with me!
So, the federal government already has procedures to catch cheats at every level.
A year or so later I switched to a dentist who was closer to my office. I told him I had had three cavities but they weren't showing up on the x-rays he took. We did two or three sets of x-rays before we figured out they were never going to show up because he had just been billing my great insurance for work he didn't actually do.
This is not possible without socializing the entire economy. At some point, you have to pay doctors, nurses, staff, equipment manufacturers, etc.
And in the US it's not.
Assuming that you can simply remake a massive chunk of the economy (hospitals, doctors, nurses, clinics, etc, etc) to be government owned is silly. People will protest, lobbyists will be paid and it won't happen. If your only solution to the problems people point out is essentially magic then, no, it's not a valid solution.
a clinic could mis-report (over-report?) how many patients they treated, and/or the procedure. They can then claim back more money than they actually spent, netting easy profit.