From my understanding Germany is an outlier among countries with socialized healthcare because their system is either straight up reliant on insurance or is modelled after insurance-like systems. My experience is based on Poland and UK. And sure in the UK you pay for "national insurance" which partially funds the NHS, but the point is that it's almost irrelevant to your coverage - as long as you live in the UK legally you are entitled to treatment, whether you pay NI or not. Again, the difference(imho) is that if you go to a hospital and a doctor there decides you need an operation done, it only goes through a cursory check to make sure the operation is covered and then it's carried out. It doesn't go to some central office where someone checks if you as a person X are entitled to have this done or not, it's not a "claim" like a one you would make with an actual insurance company.

And yes, of course you can supplement that with private insurance if you wish, but vast majority of people don't.

And yes, of course the government negotiates with providers - but when you get treated that's not something that affects you. You don't get a bill that says "your treatment was £10k, but the goverment will only pay £5k, cough up the rest". In fact no one(patients) gets any bills ever.