I sympthatise with the argument. We should test it against real world data.
Eg your argument would predict that healthcare price inflation is not as bad in areas with less insurance coverage. Eg for dental work (which is less often covered as far as I can tell), for (vanity) plastic surgery, or we can even check healthcare price inflation for vet care for pets.
I just looked it up, and apparently health care costs for pets has gone up in price even faster than for humans.
Pets typically don't have medical insurance, and any insurance that does exist there has a radically different regulatory regime than for humans.
Since 1980 for the US:
CPI has gone up by 3.16% on average per year (x4.17 in total). Human healthcare costs by 4.9% per year (x8.96 in total). And pet healthcare costs by 6.49% (or x17.87 in total).
Dental and vanity surgeries aren't happening in a vacuum. There are baseline costs eg. anesthesia, recovery medications, medical machinery etc which are all bloated due to the rest of industry not being under price pressure (rising tide lift all boats)
It's similar to how AI data center buildout race is raising the prices for consumer electronics in 2026 and beyond. The suppliers have no incentive to sell lower cost products to tiny niche