I lived for years in a rural area where my dh was the GP - was no bother to register at the next-over practice. They kept any "HCP-related" notes separately locked away, as did my dh.
Dh now is a GP in a different rural area and all his staff are patients in his surgery, again, there is secure storage for notes.
I know living in a rural area is a minefield of gossip (little old ladies calling me "Mrs Doctor" and asking for their blood test results!!), I was a teacher in the local school, my best friends in the area were the policeman's wife and the minister's wife, who understood!! But my own GP was also a good friend - that's just how it is!
I think there is a very different approach to GP in different places. My dh provides all normal GP services, and will see you the same day if needed. No dragon-like receptionists. House calls if required. First responder to ambulance calls, full GP ooh service, home hospice and terminal care, doesn't charge for passports, and does a huge amount more than "blood tests and x-rays". I know people who live in his area - I know he's very well thought of!
I'm not sure if it's because we're in Scotland where lists tend to be smaller, or what. I'd far rather a rural service - my urban practice is rotten, in 2 years I've never seen the same GP twice. But most of my health issues are related to my disability, so I tend to phone my ward for help.
The NHS are great for me - I get a drip every 5 weeks which comes in at about £8000 for medication alone each time. But it means I can walk, work etc.
My dh does earn a good wage. But he works for it. 5 years medical school. 3 years GP training. 1 night a week, 1 weekend in 5. Regular 12-14 hour days. He saved someone's life on Monday (acutely, dying in front of him!) - that's what he does.