Not in Finland I can tell you from living there after having lived in several other countries. A significant part is private, paid "voluntarily". Why would anybody pay voluntarily to avoid "extremely good" service they are entitled too?
Maybe because expectations rise with the availability of other options? Why would one pay for a Porsche when they could drive a Prius?
I live in Germany. Our healthcare system struggles a lot (mostly by design, thanks to incompetent/hostile politicians). I'd still bet the average citizen in Germany has better availability for treatments than the average American.
Most of the basic health care is Germany is not publicly organized, but private. The health insurance system is heavily publicly regulated.
I live in Finland and all of my relatives in Germany, so I see the differences very often.
This is a pseudo-distinction imho. Yes, the doctor's offices and clinics are private institutions and not organized under a single umbrella like in the UK the NHS would represent. However, the vast majority take appointments from publicly insured patients and are in compliance with the guidelines setup by the public health insurances. Also, in most cases publicly insured patients make up the majority of appointments.
Moreover, there isn't really a competition between public health insurance providers. The price difference between providers is negligible and so are the services covered (most providers cover the minimum as outlined by the law plus a few extra things you usually don't ever need).
TL;DR: the German healthcare system is public
In Germany the risk of unnecessary treatment is higher, doctors earn money that way.
In Finland being denied treatment is higher, especially for people not good at negotiating. On the appointment line they will just tell you we have no free times. Only insisting and quoting the law might help. And lying about your symptoms. Waiting for surgery typically lasts many months.
Germany spends around 30% more in health expenses than Finland.
Neither of them is perfect. But when I am really ill, the German system feels easier to work with.
The US of course spends even more in health expenses. But only a limited group benefits from most of it.
I wanted to have a particular operation and was told I could have it carried out almost for free if I waited for "about a year". Alternatively I could pay for it myself and have it in "a few weeks".
In that kinda situation, a procedure I wanted for myself, I figured I'd just pay. Certainly there wouldn't have been a problem waiting for it, voluntarily. But given the opportunity it seemed like a good decision to make.
In the past I've had work-related healthcare covering me when I had some forearm injuries, caused by climbing, which directly impacted my keyboard usage. My usage of public healthcare involved having brainscans, and other tests before deciding that I was fine. Both cases were nice and straightforward, even without adequate Finnish language skills on my part.
So I think I've had a decent interaction with all three of the systems - paid stuff, which I managed myself, public system, and private healthcare provided by my employer.
Meanwhile, for millions who would otherwise stretch to afford the latter or skip it altogether, it works extremely well, as it does anytime you just want a bed for the night (the 95% of basic medical treatments), and not jakuzi and 3 restaurant choices.
Edit: As a commenter pointed out it's 50% that use private health care, too. Very few people would exclusively use private health care.
Doesn't mean the free one can't still be "extremely good". I might pay for IntelliJ, even though a free IDE or even editor like Emacs is still extremely good.
And 40% of the population is still a huge number of people, who would otherwise had trouble affording private health care or get the shitty low tier and/or hella expensive private care afforded by the poorer in the US.
It's also not exactly like "50% of the population use private health care". It's more like "50% of the population ALSO use private health care", in addition to the provided free health care.
Well, in the end the employer has reduced your salary by that amount, employers are not known for welfare. Every employee is already entitled for full public health care. Something must be wrong with it if 90% of the employers offer double insurance in away. It's a public secret or gentlemen's agreement that employed people are not supposed to use the public health sector they are entitled to before they need specialist or hospital treatment. The gentlemen's agreement would stop working if basic public healthcare were reasonably good.
I pay for private insurance in one of the countries I mentioned to have choice of doctor and nicer hospital rooms and meant that my (non-urgent) knee reconstruction got done in 6 weeks instead of the 6 months I would have needed to wait for the same surgeon.
Your comparison does not work.