In Germany you need to make about 60000€ a year to get private health insurance (better service, lower price) OR you have to be self-employed, where it doesn't matter how much you make. (500€ private, 750€ public)

Yes, this doesn't matter for an engineer who makes about 100000€ a year. :)

But!

If you're an employee, you have to pay into a government-controlled retirement fund, if you're self-employed you don't.

If you make about 100k, you (and your employer) would have to pay more than 10k a year.

So, no, if you're self-employed and make good money, you don't necessarily have to pay "the maximum amount of social security" :)