>Singapore does not control prices (though it’s moving in that direction), it’s public hospitals are privately run,

Singapore controls prices through collective bargaining at the national level and unlike the US practically every purchase in its hospitals has to go through registration with the HSA (the country's relevant regulatory agency). You essentially cannot purchase any major equipment without running it by the national government. That's one of the reasons why the country has a very transparent pricing system.

It's not only savings accounts but also a very tight control over costs and acquisitions that keeps the price low, that's completely missing in the American system which just keeps growing.