It appears to me that these artists aren't actually naive - they have been artists for their entire lifetime and few who know a lot about art think that formal training is required for skill or understanding in art.
It seems rather that this is a particular style of painting. You can see that all the paintings have very similar composition, bright colors, similar subjects.
Probably it started off with some artists with that style being actually naive and discovered by art appreciators and then thousands of people copying that style so that it became its own thing, but it was already called naive.
I think if you really want to find art done by people who are super-isolated from the art world "Outsider art" is a more accurate term these days.
There's Naïve Bayes (although it's sometimes labeled in more explicit terms).
The problem with “unconventional” is that these works are anything but. As far as I can tell, the most of the paintings presented on the site follows a particular style. I don't think someone who is inspired to paint after watching the Joy of Painting would necessarily end up with something like this, so it's not just about being amateurish. It's also quite likely that some of the painters are anything but self-taught and have chosen to paint in this particular way.