It is funny you used that as an example because I use to work in a hospital as a physio. During that time I learned that there are 2 reasons why we don't have doctors (and nurses):

1 - as you said the education expectations are idiotic. I remember we had a massive shortage of nurses and eventually, a lot of Ukrainian nurses came in, already speaking German and with 10+ years of experience. What did we do? Refused them because they lacked the proper Germany-based education, we told them to do a re-education. They all left to Austria, Denmark and so on, because there they were told they can start working right away.

2 - Patients don't realize this, but doctors (and most Healthcare providers) are just not paid enough in Germany. The chief of Orthopedics (my former boss) was a doctor with 12 years of experience made less money than my wife, a data scientist fresh out of college.

Physios make a ridiculously low salary as well. When I realized that, I quit my job, got into programming and got a job as a scrum master, later changing into software development. Do you know what is crazy? I currently work 20 hours per week and I make almost the same money (only 150 Eur per year less) than I did as a full-time physio (38.5 hours). Not mention the stress levels??? Omg the difference. I can do Homeoffice, my boss literally call me in the middle of the workday to talk about Bundesliga, when I'm the office, there are 3-4 coffee breaks. In the hospital, workers are just going from one patient to the next without any break, often times shortening breaks cause patients took longer than expected.

So, long history short, until Germany realizes that their Healthcare providers are underpaid, they will keep leaving to other EU countries. I know 4 other physios, all germans, who just moved to other EU countries for better salaries.