I just wanted to add a story as well - my dad was diagnosed with a very rare type of stomach cancer called GIST about 15 years ago in Poland. At the time, he was one of ~6 other people in the entire country with this diagnosis, and the diagnosis was....bleak to say the least, I think the doctors were cautiously giving him 6-12 months max. However, company Novartis has just certified their "Glivec" drug specifically to use against GIST, since it targets the same cell pathways. Now, the problem - Poland does have nationalized healthcare, but Glivec was
insanely expensive - basically a box of Glivec cost around as much as an annual pay for many people in Poland at the time....and my dad had to take two boxes per month. And no, because it hasn't been proven to work against GIST yet, it was not on the list of refunded drugs - so my dad was placed on a controlled trial conducted by the largest oncological hospital in Warsaw, where the study funded the drug for him. Long story short - the drug worked miracles, my dad not only recovered, he lived another decade after that(died of another cancer that sadly didn't have a miracle cure this time).
But - other people in this study didn't get the drug. I don't know if they were given placebo or just something else instead. My point being - they didn't survive, my dad did. After the study was concluded, the drug is now paid for by the national health service and anyone who needs Glivec can get it.
So why isn't this a critique of the nationalized system? Well, because the way I see it - in a private health care system, no one in this group would survive, because no one in Poland could ever afford this treatment. At least some of the people were still given a chance because the system has enough flexibility to at least try new and experimental treatments.