Over the last number of years socialist policies have become very popular in the US as a "fix" to its healthcare woes, but it's also clear that the current system is not working either. Have any great Catholic thinkers written on what an ideal healthcare system in a country should look like?
I don't think it takes a great Catholic thinker really, mainly because without the intervention of Holy Mother the Church, insanely high prices for everything health related will be the rule.
Back when the Church was the authority, She was respected even by crooks, and insurance, no matter who or what was insured, used to be only a fractional expense, and then was only to be relied upon in rare or unusual cases. People were almost glad to pay for and be insured while never having to use it at all, but that whole line of thinking has vanished from existence because the market is simply way too profitable for the doctors, hospitals, big pharma insurance companies and on and on.
Figure out how to quell the greed, and prices would be affordable for pretty much everyone. Not gonna ever happen without Holy Mother the Church though.