Exactly! This is what no one in the US seems to understand. My encounters with private clinics and hospitals in the UK (all 10+ years ago, at this point) were unbelievably luxurious, at prices that (totally, completely free-market driven, mind you) were affordable on middle-class incomes. Or, yeah: there's private medical insurance, also free-marketed to "shockingly reasonable", by US measures. Americans on good salaries have been bamboozled into believing that a single-payer system will trap them into some kind of hell-hole hospital° with no recourse, when in fact the exact opposite is true.
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°And, of course, the "hell-hole hospital" examples are cherry-picked. Bad on their own, of course, but not representative of a system as a whole, nor recognize that equally awful anecdotes are abundant in the USA.