Another important part of the doctor-patient relationship is actually having a relationship. It's recognised how important continuity of care is, and that it can tangibly affect patient outcomes, yet GPs don't have the resources to make that happen.
It's the difference between going to the GP about, say, your GI problems, and either
a) feeling able to trust that they know you and care about you, having had them treat you before for other things and seeing them care for your mum through her final months, having them say to you "I know how much pressure you've been under at work and how difficult things have been since your mum died, I can't find a physical reason behind your symptoms but sometimes these things can happen as a response to stress happening in our lives"
or
b) having some bloke with a medical degree who you don't know from Adam and you know you'll never see again, telling you that he's given you all the tests you wanted and there's nothing wrong so it must be stress-related.
If b), you're far less likely to feel reassured and more likely to keep going back IMO.
I don't think it would solve everything, GPs would still have their frequent flyers, but it might help.