We've been with the same GP practice for nearly 40 years, though obviously all the doctors from back then are now retired. Right from the start we had a named GP but it never made any difference to who we saw. For emergency appointments you take pot luck who is available, for more planned appointments you can choose which doctor you see but you have to wait longer.
About 10 years ago I wrote to the practice to say my daughter and I weren't able to get to the practice. After some correspondence they agreed we could have a home visit every 6 months from a GP of our choice to review our ME/CFS. In that correspondence they were also open about not knowing anything about ME and not seeing that they should since there is a clinic (run by OT's) they refer people to. They said they are generalists, and can't be expected to know all about specific diseases.
I nominated a GP I'd never met simply because my daughter preferred a woman doctor. The GP I selected is very nice, and does home visits when really needed but only works part time and is clueless about ME, so I've abandoned the 6 monthly ME reviews. We now only use her for other things, not for ME. Most of our consultations now are by phone or in writing online via their system, especially since Covid. I've even sent photos when necessary by smartphone. Home visits only when really necessary. She has written letters to support our benefit applications saying basically what I asked her to say - confirming diagnosis and summarising what we can and can't do).
My conclusion is that most GP's are clueless about ME, and I agree it's more important to have a GP who listens, takes other non ME symptoms seriously and is willing to do home visits if you're housebound, and has a sensible appointment system where you can at least get a phone appointment on the same day if needed.