This is not an equivalent comparison.
In Europe many cancer treatments are simply not paid for by social health care, because it's too expensive or experimental.
Rich people still go to private health care providers for more niche treatments, or simply for shorter waiting lists.
What you have in Europe is - long wait lists, for everyone, and fewer numbers of actual treatments (plus many things not covered by social health care, e.g. dentists)
What you have in US is - no wait lists, healthcare that's probably 2-3x as expensive, but you actually can get the best of the best treatment if you pay for it
Clearly for poorer layers of society the US system is bad. But for society as a whole I would question which system is actually better. They both have bad and good parts.
To be honest if the US actually implemented a real market system for health care, and prices would drop a bit (with the kind of stuff Mark Cuban is building), the US health system would be FAR superior than Europe, even if its not free.