No, sorry, you pretty much have it 100% wrong.
You seem to think the problem with healthcare is that everyone is not 'included'. That is very very wrong, and pretty much what the healthcare industry wants you tho think, congratulations at swallowing the hook, line, and sinker.
The problem with healthcare is that an essential service, and one which is NOT optional for people, is run at a massive private PROFIT for the incumbents.
They have, for a long time, worked with the government to massively regulate out any form of competition, and are currently working to regulate in all users to maximise profits.
The WHOLE reason Us healthcare (and many others) is so catastrophically overprices and inefficient is that it is run PURELY for profit, and regulated for protection of that profit. Whoever people have little choice about using healthcare - your other choice is being sick or death..
People think regulations are used to control the providers, however it is almost exactly the opposite - regulations exist to stop competition from new providers, and to make sure only the massive incumbents are allowed, and hence there is no real competition.
Compare the costs of healthcare to unregulated services available in Asia, which often provide better service, with the same or more advanced capabilities, BETTER patient outcome records, and at a much MUCH lower price... Good examples are South Korea and Thailand private medical services.
Your governments and your Health companies (providers, insurers, and overseers) and using your health to empty your wallets, and letting the people without enough cash simply suffer, as a scare tactic so they can squeeze the rest harder. Land of the free! ra ra!