To be honest, I prefer the current system which has been operating at our GPs surgery for a while.
Getting an appointment used to be a nightmare. You had to ring at 8.30am but you were in a long queue even if you could get through. Or you could go in person, but people turned up earlier and earlier and the queue was enormous. Either way, the appointments were usually gone when you managed to speak to a receptionist.
Now you write out your problem and say whether you want a response by email, phone or face to face - except you don't get the latter during Covid, unless it's vital. I prefer a chat on the phone in my own house rather than sitting for ages in a waiting room, just to say something I could have said on the phone. Obviously, if you have something which has to be felt, like a lump, then it's different.
I don't worry about privacy. The surgery staff have access to all your records anyway if they are interested, but I am sure they are not. As for one's nearest and dearest, I often have to go with DH to appointments because he doesn't tell them half of the relevant stuff or ask any questions. When he has a phone consultation, I can prompt him in the background.
I had a hospital phone consultation recently and it was brilliant. 10 minutes discussion and then done, instead of spending ages trekking to hospital and sitting around.