It is not so obvious at all. Medicare Advantage does not have price controls, and it still costs less per capita than Original Medicare.
> A dead simple “this is how much you’re allowed to charge”.
This has its own set of unintended consequences, including physician rationing (it's a huge crisis of the NHS right now), and a reduction of investment in new medical research. There are many good reasons to be against introducing this in the US.
Switzerland does not have price controls on medicines, treatments, etc. and the reason why it is so often cited is because it enjoys a comparable level of healthcare innovation to the US while still ensuring universal access (through its ACA-like subsidies). It also costs a lot per capita (among the highest in the OECD), but it actually gets what it pays for (https://pubmed.ncbi.nlm.nih.gov/26766626/) (https://www.theweek.in/news/world/2022/05/07/7-reasons-why-s...)
In fact, of the countries that usually make up the global leaders in health/medical innovators, all but 1 (the UK) engage in price controls (https://immigrantinvest.com/insider/the-best-healthcare-coun...), and the UK's NHS is suffering from a rationing crisis, and (ironically) a cost crisis.