I have an interest in fiber arts.
As a professional pet groomer, i've saved a lot of very nice undercoat from dogs and cats to spin. It makes a really amazing yarn. Dog hair is warmer than wool. So is angora rabbit and I am guessing that cat is as well. Dog hair has some different properties from wool (it doesn't have the scaled a strand of wool has so it doesn't lock into it's self for instance).
Most hand spinners that work with it on any sort of commercial level card it with wool to give it elasticity.
I've spun dog hair but not cat hair. I don't have enough cat hair to work with yet. I don't save any cut hair. Once you cut the coat, it has a blunt sharp end. This can make for an itchy garment in a sensitive person. A hair that has naturally been released due to shedding does not have this blunt end. I only saved undercoat - the fuzzy very soft insulating layer, avoiding any guard hairs (the coarse outer coat) and any cut coat.
You'd be surprised what hand spun speciality fibers sell for!