Seems to me that all visits to the GP should be reported to the medical branch of the licensing authority. That way the disconnect between GP services and operational requirements can be eliminated.
In Canada at least, there are reportable conditions that a GP
must report to Transport Canada. I am also obliged to self-declare GP visits on my medical when I visit my AME.
The problem is that not many GPs know this (not even my wife, who is also a GP, until I told her). A couple of years ago I was diagnosed with Type II diabetes, and I had to walk my GP (not my wife!) through the reporting procedure (it has to be the doctor, not the pilot, who reports, if it's picked up between medicals). He was completely unaware.
Fortunately we did it all by the book and since I'm not insulin dependent and otherwise very fit (4500 km of cycling a year) I still have my medical though I was grounded for 3 months while sorting out the medication and undergoing a battery of extra tests to satisfy Transport Canada. And this is for a PPL (class 3 medical), not an ATPL (class 1) like most of you guys.