Maybe its just the doc offices i've been to, but i think this would actually just increase the patient churn in a hospital. There's no way a doc is going to increase their patient time by the 40% saved if the hospital can toss them in front of another patient.
It's definetly not just you... Tho that may still be a plus considering the shortage of doctors in a lot of countries. But the privacy concerns still remain.
Use the built in backup and restore and you dont lose your groups. Signal's primary design direction is encryption and privacy, you're going to have to compromise somewhere.