> certain professions like government workers, doctors, etc. have their own health insurance schemes <

Completely WRONG: you are mixing up "job-dedicated" pension schemes like for lawyers or doctors with the healthcare setup - in healthcare, there are only two parties: "public" healthcare ("GKV") and "private" healthcare ("PKV"), these two types are not anyhow related to the job dedicated pension schemes.

Correct is, mostly all politicians, high-earners, docs, lawyers etc. are chosing the "private" insurance version, for (at least until yet) several benefits compared to the ones using the "public" model.

You are allowed to enter the private model above a certain salary, but you are not forced. It may be cheaper for some time, but at least if kids arrive it gets fucking expensive, since in the public model your children are insured for free,while in private mode you have to pay for them.

Also handling private mode insurance is more work.