I don't live in a healthcare system where any of this matters. I live in a universal healthcare (insurance) country. I can go to any hospital and any doctor "for free" at any time. I don't care about their other doctors in the slightest, I have my list of trustable doctors and where they work based on personal merit. I always pre-check my doctors on the internet before I visit them. I don't even know the names of the hospitals I visit, to be honest (often it's just town name anyways). However most often the hospital nearest to me is the one I visit because the standard of care is good enough - now I will go a little (2 km) further to visit this one. I wouldn't go more than 5 km out of my way to visit a doctor (obvious exceptions apply).