YANBU, I'm also a teacher and totally feel your pain. As has been acknowledged, it is also the same for a lot/most working people.
My surgery got rid of online consult because it was overwhelmed (because getting through on the phone is like trying to get an audience with the pope!).
So, if you want a same day appointment, you have to ring at 8am. It typically takes 40-60 minutes to get through.
Except I can't do this because my school starts early, the kids line up at 8.10am and I have to collect my form group. So, I then have 30 children in front of me and cannot make/take calls.
I tried, several times, to explain this when I have rung later in the day but it doesn't go in and I just get told 'well, you have to ring at 8am'.
Luckily, I am not often unwell! Last time, a few months back, I knew I had infected tonsillitis as I could see it. I realised mid morning on a Friday. Didn't even bother trying to GP - I did 111 online at lunch as I knew the call wouldn't come before I finished teaching. Managed to get a call back and prescription sorted really easily.
Similar issues with less urgent appointments. I rang a few months ago as I needed an appointment to discuss a long term, complex spinal issue. I got an appointment but it was 5 weeks away!
My dad is at the same surgery and has a repeat prescription. He has now been told he cannot ring for it, he must use the NHS app ( which he didn't have - technology isn't really his thing!) Or he would have to go to the surgery in person and request it that way! I downloaded the app for him and showed him how to do it, but not everyone will have that support.