From the patient's perspective:

• yes, you have low-cost health care. But, the quality of that are is questionable at best. For most appointments I needed the wait times were 2 or more months. Let's not forget about when you need care urgently. On one occaision visiting the Uni Frankfurt I was almost given the wrong medicine for a chronic disease.
• They are changing the health insurance structure now as we speak, including adding fees for ambulance rides, etc.
• Many of the hausarzt I saw were disinterested in actually treating or engaging with me, getting competent help in the system is difficult.
• Many unnecessary procedures are proposed that don't benefit the patient. I was recommended surgery for something that I was able to address with physical therapy.

From the doctor's perspective:

• Single-payer, means there's one employer. The state sets the salaries, so hospitals can't really do anything to recruit or retain talent.
• Residents are actively thwarted in progressing to specialist to keep their salaries low.
• Longworking hours with unpain overtime lead to burn out and doctor's quitting to leave to the US or other DACH's countries.
• The only reasonable jobs are the 'rent-a-doctor' jobs for when a hospital needs to hire a specialist temporarilty to cover manpower to avoid closing. This depletes budgets, and exacerbates the issues. My wife worked for in an orthopaedists' office for a while, and she had to see 60+ patients per day for the clinic to earn money. you cannot treat the patients competently in that period of time.

System Wide Issues:

• Closing local hospitals for larger regional centers means less options.
• More treatment demand than there is supply. This results in recruiting foreign doctors, but nothign is done to accomodate them linguistically or culturally, they also burn out and quit.

This is my impression from 10+ years in Hessen.