edit: I also went from dirt-poor (and I'm assuming really horrible) health insurance plans in the US to having ridiculously good private insurance in the UK, so I'm already aware I'm entering into a supremely Apples v. Oranges scenario as is.

I've lived in both the US and the UK (well, the Isle of Man; I've heard NHS is much more of a pain in the ass in the mainland UK), and I'm just shocked at how awful the customer service has always been in the US.

In the US, I have never arrived at a doctor's appointment without waiting far past the time the appointment was scheduled to start and then waiting for the GP to actually come to the appointment room once you're seated there. In the UK (so far), I've seen the estimated time left before my appointment on an LED screen, and then both been led to the room on time and had the GP come in almost immediately.

In every aspect of healthcare in the US, I've been shocked at how long you're just expected to wait for absolutely everything.

Even if you arrive early, you sign in, wait in a room full of sick people for (on average IME) 40+ minutes past your appointment time, and then you wait an additional 15+ minutes for the GP to actually come into the room to begin the appointment.

It actually makes me physically angry to think about how much time I've spent waiting in a doctor's room over the first 20-something years of my life.

In your scenario B), I'd expect to be able to book an appointment online, arrive two minutes before it's scheduled to start, and walk out fifteen minutes later with whatever result you were looking for 99% of the time.

To be fair, I've visited my general practitioner exactly twice since I've moved here, so I have no sample size; and as I previously stated, I live in an area that has a reputation for having much better healthcare than the mainland UK.