It's just that private health insurance isn't really a thing in Europe.
Not true. Depends on the country, but some have private hospitals and insurances and everyone who can afford it buys it, to avoid waiting lists.
Source: Live in Europe, has private insurance. As I recall, it’s like a fifth of the country that has it here.
UHC works in rich mostly homogenous countries. Arguably it would have worked well in the UK had the UK not decided to import all of the dregs from the decolonized Empire.
UHC, like all kinds of government welfare, only works if everyone pays into the system and the government doesn’t import millions of foreigners.
That’s also why European countries tend to have strict migration policies.
There are many ways to do healthcare, but the bottom line is this:
Healthcare is a limited resource that you either ration by money. Or time.
If you ration it with money, like they used to in the US before Obamacare, everyone who can afford it get good care.
If you ration it by time, like in single payer/public systems, everyone gets a kinda shitty system where medical care won’t bankrupt you, but you may have to wait weeks, months or years for surgeries and appointments (like if it’s a specialty field.)
Also: Another issue with public healthcare is that it invariably ends up as a political football. The major way to pay for it (aside from co pays) is taxpayer money, and politicians hate raising taxes.
So before every election, you get these gay fights about moving around 1% or 2% of the budget to pay for cancer surgeries instead of psychiatric care or whatever.