I once was looking to get a cat and found the goofiest looking idiot on Craigslist. Turns out, it was a purebred Exotic Shorthair that was surrendered to a shelter because it didn't look fucked-up enough (it could still kind of breathe through its nose). New owners wanted to recoup costs because they adopted another cat that was "more playful" and the exotic was getting eye-goop on their white carpets. A wonderful standard for purebreeds!

I changed his name from "Luigi" to "Waluigi", and he was best best buddy for many many years.

Not necessarily? More like by default. Purebreds are a thing because of certain genetic traits and are bred to not only maintain them, but to enhance those traits. Because of all that inbreeding the propensity for certain diseases and cancers are vastly increased. A purebred dog or cat will with near certainty be riddled with cancer or disease by the time they start getting a bit older. I love both cats and dogs, but purebreds shouldn't be a thing.