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.
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
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).
But dental and vanity cosmetic surgery have gone up by that metric. Dental is less covered by insurance for most people. Vanity cosmetic insurance is covered for almost no one.
Vet care for pets has gone up a lot more than healthcare for humans.