tl;dr: All of my comment is basically agreeing with rndgermandude that the OP's description of German medical care is not accurate.
I co-founded a company that sells practice management software to primary care doctors in Germany. We work closely with the Hausärzteverband -- something like a union for primary care physicians -- and I speak with doctors in Germany, board members of the HAVG, and so on basically every day.
Germany has three different medical/insurance systems -- KV, HzV, and private insurance -- I worked with HzV so am most familiar with that but everyone has at least a passing understanding of KV as well since it was the only one until recent decades. HzV is more popular in certain geographies -- for instance if you work for Volkswagen you'll be in the HzV system and not the KV system under a BWQ contract.
I've never met a doctor in Germany that doesn't have staff. A quick check of the analytics of all the practices using our software doesn't show a single one.
As rndgermandude says, every single one has at least an MFA (and nowadays probably a Vera as well, since they can earn extra money that way). Our analytics shows 2-3 MFAs per doctor is the average but there are always edge cases.
>They prescribe whatever they want
This is not really true. Every insurance contract will have different rules about what can be prescribed. They can't FORCE a doctor to follow those rules but they doctor is monetarily incentivized to do so. For instance, getting a bonus every quarter so long as 80% of their prescriptions follow insurance company rules. The checks are done at run-time, every doctor knows instantly if a prescription is against insurance rules, and practice management software is REQUIRED to suggest alternatives that meet insurance requirements.
>they're guaranteed to be paid in a week
Doctors are basically NEVER paid in a week. They submit their billing at the end of the quarter (here I'm speaking primarily of HzV contracts; I'm not sure how the third option -- private insurance -- works) and then get paid a while after that.
>no questions asked.
No, this is not remotely true.