When I arrived at the aiport, I didn't have to wait at all. I have been booking a small SUV (CFMR) from Flizzr/sixt at the aiport directly. Although I had the full insurance package, I was advised to take the insurance from sixt, but in a kind and professional manner. Since the costs are too high (18 €/day) I declined and took "the risk".
The only negative aspect I can tell is that the brand new car (Duca Duster) already had two damages. One obvious scratch on the front bumper which has been shown to us as the only damage of the car. I found another scratch on the left front door which has not been mentioned by the employee and the report of the car.
When we returned the car, it was checked very precisely by the staff so I assume they would have found this damage and charged me. I have not had the feeling that they were trying to scam me this way, but in the end: who knows.