My current GP and the whole surgery is incredibly good. Appointments when you need them, great care, timely and appropriate referrals. I've been a patient at various places (moved a lot) and have never seen anything so good.
I'm fairly convinced that a big part of their success and ability to give such excellent care is their very effective triage. Some people hate it because a receptionist asks you questions when you call (yes they are trained to do so, and have software to help, and are caring and professional with it) and then they give you appropriate advice/appointments.
If you don't need a GP, you won't see one. You may get a nurse, nurse practitioner, some other clinician, told to speak to a pharmacist, given self care advice, etc. They also handle queries by asking a GP and getting back to you, no app needed. Phone apps where appropriate.
But then when you do need a GP, you're in super quick. Where possible, with the GP who has a special interest in your problem. They offer (without being asked) double apps for big problems.
No idea how they manage it TBH because it must be hard to stay firm with people being all entitled as OP describes. You can imagine the abuse. But I think everywhere is going to have to adopt this model, and folks are going to have to learn what they can take care of themselves and what actually needs a doctor.