The price rises are due to this. See
https://www.theatlantic.com/magazine/archive/2009/09/how-ame...
Note how prices for Lasik eye surgery, which has little government involvement, have trended down dramatically.
Either way, we need price transparency before people start acting rationally, and government regulation of irrational spending is going to be wasteful. Price transparency would make the promise of single payer (government) healthcare actually sustainable for a populace; without it, you’re just making the healthcare industry richer without actually providing a proportionate amount of care to the public.
See "Competition and Monopoly" by Frecht.
The supply of drugs is heavily restricted by patents and the FDA. See "Regulation of Pharmaceutical Innovation" by Peltzman.
Meanwhile, government is the only meaningful access many have to healthcare and education.