I know it's probably a bit exaggerated on purpose but also in European countries it's definitely not zero. We are in a significantly better situation than the US, that's fot sure. Our problems aren't remotely comparable. But also here, it can happen that certain treatments aren't covered, also here there are (few) people without health insurance and also here people can lose their job or never find a job in the first place due to illness related issues or disabilities.
There's also the issue of waiting times - you might need care somewhat urgently, but need to either wait for multiple months or pay (or hope that when the issue becomes more immediately life-threatening they can handle it in time). Public healthcare isn't perfect, and at least in many places still needs a lot of work.
I always dislike this take because it pretends the US doesn't have this exact issue. I've known people with less than ideal insurance who had very few doctors to pick from in-network and would take months to get an appointment.
Long wait times still happens in the US. Just like it can happen in public healthcare.
I take issue with 'needs a lot of work', though it is common phrasing. It promotes the false idea that 'business is more efficient' by making it sound like the public administrators are too dumb to know how to do their job.
The real issue, in most jurisdictions, is that it needs more and stable funding, and less political interference.
Well that and not to mention that politicians abroad do the exact same thing they do in the US. I know the British for instance have a Conservative Party that have repeatedly attacked their healthcare system in order to make privatized insurance seem better.
And then the issues caused by a lack of funding get used in the US to say “SEE! This system doesn’t work!”
Which is the logical equivalent of watching your friend baking pies with not enough filling and deciding to instead pay 4x the price for a pie that you won’t even get your promised slice of. Oh and the pie you get occasionally is made with the meat of other people who were also promised a pie and paid for it.
In several countries the mainstream party politicians (who are Neoliberals) have been slowly privatising healthcare by forcing the Public Healthcare System to outsource more and more of the work to the Private Sector and using the same technique as Thatcher in the UK used to privatise railroads (of which now, decades later, you can see the horrible results) - defund the Public Service and when the quality falls because of it claim that the Public Sector is always incompetent and the the Private is always competent so that's why that Public Service had problems hence it needs to be privatised to improve.
On top of that there is the actual genuine problem (rather than artificial meddling with the Public Healthcare System to send more money into the hands of politician's mates) that populations are aging and older people require much more Healthcare Services in average.
I don't mean it to imply lack of competence, and both issues you mentioned sound like they'd qualify as that "work" for me, notably would probably need legislations drafted and passed. Bureaucracy is slow, but hopefully things will steadily improve.
Notably, public institutions are gonna be inherently tied into politics, having to deal with bureaucracy to get things done and subject to the whims of politicians playing their games for influence. It's not that public administrators are dumb, but they're part of a much bigger system that is funded by public money, and that presumably makes everything harder.
One big issue is that, to my knowledge, there simply aren't enough doctors. That's not something that can be fixed just by working more on it, but hopefully it could improve with better technology and more funding!
I will also say, I think one issue that can be improved rather directly is coordination - some private institutions can give you a list of timeslots available to sign up for and receive you in your allotted time, but in other places (both private and public) you might be waiting an hour for the doctor to show up, with no information on what's going on and three people ahead of you. Shit happens, but it seems like the systems in place are severely lacking, if present at all.
Waiting times are atrocious here in the U.S. The earliest in-person appointment that I can get with my GP is about 6 months out. Non-urgent surgeries are sometimes take close to a year. A friend recently had to keep a bladder drain in after surgery for an extra week because there were no doctors who could do the 5-minute removal available.
Anybody who says that long wait times are unique to public health systems is lying.
Wait times are a factor of the number of doctors though. Like in the UK private health insurance may let you skip the queue, but that's only because there's relatively few people capable or willing to take up the private slots. If everyone had health insurance then the "faster" pathway no longer exists (or more likely people who're willing to pay more skip the queue).
The good thing is that it creates a great competition for the privates. I have a very good insurance for 1K a year. No extra payments. Can go as much as I want. Many locations included.
For "small" or "quick", I go to the private one. Saves me time and reduces waiting times for public.
I've lived in a couple of countries in Europe and some have Universal Healthcare systems (such as the UK and Portugal) but others such as The Netherlands and Germany have Mixed Systems with Health Insurance but highly regulated and were some people can get Health Insurance from the state.
You're not going to go bankrupt from the treatment or get treatment denied in countries with UHC.
However if you lose your job or never find a job in the first place due to illness related issues or disabilities you'll almost certainly end up on benefits which again can be better or worse depending in the country.
I would say things have been getting worse all over Europe (personally I think it's exactly because there's been too much copying of shit from the US), especially when it comes to the level of benefits for poor people being sufficient (the house prices bubbles all over the place and the lack of building of social housing have made this a massive problem in most countries), but that's not the same as simply going bankrupt from medical bills because you've had an accident, ended up in an emergency ward and got a life saving surgery.