"Avian vets nearby" was one of the first things I would search for when we were looking to move. Going from a suburban city of 35,000 to a no-stoplight town of <1,000 means that I was going to have far, far less resources in my immediate area. It was super important for me to know what vets were available and how far away they were. We have a fair few vets in a nearby town (~30 minutes away), but the closest exotic vet is an hour away.
If you're planning on moving, just like you would check schools for your kids and access to grocery stores and other necessities, do your research on the vets local to where you're looking to move. You absolutely need to have a plan for when/if things go south. Knowing exactly what you're going to do when/if your animal gets sick is a vital part of ownership. You should never wait until your animal is sick to start doing research on what vets you have access to. Get phone numbers and hours of various vets within a few hours' drive and keep them handy in case of emergency.
This is exactly what I did. Happily, my workplace and one of the UK's leading exotic vet practices are fairly close to each other so it was a relatively easy decision to make. If it wasn't for Leia then I'd probably live somewhere cheaper but with a longer commute, but I want to a) maximise her time out of the cage which would be difficult with a 1hr+ commute each way (not unusual for London) and b) be close to an avian vet. So here I am, getting my bank account gouged on a monthly basis
I do think it's worth thinking about the huge changes in veterinary medicine over the past 80 years or so. Alfred Wight (better known under his pen-name of James Herriot) reflects a lot on this in his writing. When he trained in the 1930s, he was even taught about urban working horses. Much of his initial work was on farm animals - agricultural draft horses, cattle, pigs - and usually getting kicked about or generally mauled. Cats and dogs made up a relatively small proportion of the practice and exotics would be unheard of (despite parrots being kept in the UK). He documents the massive changes in the veterinary profession over fifty years - the introduction of sulfonamides, antibiotics and even more sophisticated treatments, the phasing out of draft horses in favour of machinary, and, crucially, the popularity of cats, dogs and small animals. I think we in the US, Canada and Europe sometimes forget that other countries have very different veterinary priorities and resources, and that not so long ago, we too would struggle to get vet care for even a cat.
That said, I do think there has to be some initial research on veterinary care when you're working out whether it's feasible to keep a bird. It's as important as working out what cage you should get or what you should feed. If you
know that there isn't avian care in your region or that you'd struggle (or simply don't want) to pay vet bills, is it really responsible to get a bird?