This is a highly controversial issue. Many of the diseases against which pets are inoculated are transmitted by other species, so just because your cat never meets other cats doesn't mean he could not contract one. I don't know where you live, but there are raccoons and foxes practically everywhere in America, and they are very common carriers of rabies and other fatal diseases. Opossums, skunks and rats also carry a lot of crap, even mice. Cats who never go outside are at substantially lower risk, and some veterinarians now recommend against many of the vaccines for them.
Of course you will encounter cats who never got their booster shots and had no problems. This is a public health issue, which is all about statistics. If only one cat out of a hundred dies of rabies, that would be about a million cats in the USA and we would call it a national crisis, even though your own cat would have a 99% of not being one of them.
One of the reasons your family's cat didn't get FeLV or distemper is that most of the cats she came in contact with
had been vaccinated. You were basically freeloading on the money your neighbors spent on their shots. Don't try that in some place like Bangla Desh. Public health works on the principle that there will always be a few people who don't get with the program, but not enough to cause an epidemic because there aren't very many unvaccinated people (or pets) to transmit it to.
We haven't had cats in twenty years so I'm more familiar with dogs these days, but most of the vaccination protocols are the same. Rabies is a three-year shot, and many animals don't need it quite that often. You can get a vet to do a blood titre and determine whether your cat needs a booster, but the test will cost more than the vaccine. People do that who worry about the side effects of the vaccine and are willing to endure the expense. With twelve dogs we tend to err on the side of economy so we just get the dang shots.
As for distemper and all the other stuff (in dogs it's hantavirus, leptospirosis, parainfluenza and parvovirus), that is an annual vaccination, everything combined in a single shot. If you object to the expense, you can order them yourself from a place like PetCareRX or Drs. Foster & Smith and it becomes so cheap that you stop worrying about it. It's not hard to give shots these days, you don't have to find a vein.
If you object to the medication itself, then you have to do your own risk analysis. A couple of our dogs have had bad reactions to the Lepto, and apparently that's not uncommon because the combined vaccine is available without Lepto, DHPP instead of DHLPP. We had a cat die of FeLV before they had a vaccine, and when I was a kid my dog died of distemper (I don't think they had that vaccine in those days), so I tend to be a big fan of vaccinations unless there's a compelling reason to avoid it.
To reiterate, don't think your cat is not at risk because there are no other cats around. Most--if not all--of the things they vaccinate for are transmitted by many species of animals, and they're all out there. Probably a whole lot of them if there are no cats around to kill 'em all.
But to be fair, there are good people who disagree with me. Perhaps one of them will speak up.
BTW, a lot of diseases are transmitted by fleas and ticks. You should absolutely use Advantix to keep your cat free from parasites, especially if she goes outdoors. Lyme disease is fast becoming an epidemic in many states, and it's transmitted by ticks. Mosquitoes carry West Nile virus, and Advantix repels them too (but not FrontLine and some of the other treatments). This too is something you can buy very cheaply from one of the online pet care catalogs. It's absurdly easy to apply, just comb the fur away from a patch of skin and pour it on the skin. You don't have to send some veterinarian's kids to college by paying him to do it.
