You first write general things about the concept of insurance, but when you go into details it seems you are talking about very specific aspects of certain national health insurance systems, that are unrelated to other types of insurance (or health insurance in other countries). Or am I mistaken? In many insurance situations the provider of services doesn’t even have a say because the insurance pays money to the insured who then pays the service provider.
It sounds to me as if this is the umpteenth proposal to reflect contracts between businesses in OSM: This shop is part of this coupon redemption scheme, that doctor has signed up with this insurance, and this vendor uses that payment processor.
I am against modelling such detail in OpenStreetMap because it is mostly fleeting. These alliances can change willy-nilly.
If I want to find out which doctors I can go to that accept my insurance, then my insurance should be able to give me a list of their current business partners - and I can then find these doctors on OSM. Instead of OSM trying to model those business partnerships.