Because they aren't public. They are provided by a company.
> And let's not mention the health care system, which literally has two tiers, one for the poor and one for the rich, with of course the poor-tier being barely functional, and still expensive as fuck
This is because of inefficiency, an aging demographic and regulation, not because of capitalism. The "system for the rich" was worse back in the day, and only became "better" for doctors because they adjusted their rates for covered services. In fact, because the "poor tier" insurance companies have not adjusted their rates according to inflation for a long time [1], services are of course getting worse. The average dentist earns 50% of what he earned 1970 adjusted for inflation. [2] This is called the "Punktwert", it hasn't changed since 1980 ([3]) and it is the single most important factor why services are getting worse and worse. No one is getting rich off of GKV members. Not doctors, and certainly not insurance companies.
> "Social market economy" my ass.
Sorry, no. This is the direct outcome of a social market economy, when the economic motor isn't doing so good, you still have to pay for permanent social gifts that were given to the largest voting class (old people). The government mandated insurance companies are close to being bankrupt because of this exact policy. In fact, they would already be bankrupt if we didn't have a social market economy [4], which pays billions of tax dollars to prop them up.
> The only people getting any kind of social benefits are the retired boomers and if you were to do the accounting, even they got massively shafted by the capitalists, because those boomers would be 3x richer if their lifetime savings were properly invested.
Well, boomers, pensioners and those close to retirement make up 60% of the voting base. They got what they voted for, good and bad, a social market economic model that bleeds the workers to pay for pensions. That matches the definition of a large welfare system exactly. They also voted pretty clearly against an investment backed pension scheme and have been voting like this for 4 decades now. As always, economic models have disadvantages, and we are finding out now that models close to socialism stop working when you run out of other people's money.
[1]: https://www.aerzteblatt.de/archiv/amtliche-gebuehrenordnung-...
[2]: https://praxis-analysen.de/das-verfuegbare-zahnarzt-einkomme...
[3]: https://www.aerzteblatt.de/news/mehrere-vertragsarztliche-le...