That would be interesting data to take a look at. I assume most use lemmy similar to myself, where you mostly scroll through all federated instances and don’t pay attention to the source unless necessary (except lemmygrad). But I’m open to being proven wrong.
Don’t forget the possibility of refusing to identify yourself. Without an identity there is no way to bill you. So you just leave and the hospital has no way to contact you. This is the path taken by many, especially the poor.