Why should I get less than full health care if I pay the same income taxes and health insurance (15% of my wage on it's own)?
If you restrict services to permanent residents than restrict the taxes we pay as well (btw I'm 100% certain I pay more in taxes than I consume in benefits, and Germany didn't even have to pay for my education or early life).
I'm not saying restrict services to non-citizens, I'm saying do not have the government pay for those services for non-citizens. If you pay a private company for health insurance then you should be covered by that insurance for the things that the government won't cover.
This is one easy way that the government could cut health related costs.
But I am paying for these services, with 15% of my salary. Why should I have to additionally also pay for private insurance?
No, the Government of the place you are living is taking 15% of money out from your salary to pay for the services that it provides to both citizens and residents. It does not have to divide equally between the two groups.
In general I would say that most of social safety net benefits should be applied to citizens, and then be scaled down for the other groups of people living there.