I think between us we're onto something in our explanations. The initial lack of symbolizing in the Gothic world that I was talking about- a real handicap because they certainly liked to interpret things symbolically. And artists used copy books as the source of a lot of their animal figures. If cats weren't in there then that wouldn't have helped either.
Later on we get the Familiar stuff which others here know more about than me. But that sounds plausible too. Hogarth is happy to use that in The Graham Children but in other respects it must have been a hinderance.
We seem to be dealing with a pretty narrow range of artists here, certainly in finished pictures, though less so in sketches. It's hard to understand what stopped Leonardo, Delacroix and Gericault taking their sketches into finished compositions. Renoir and Balthus both seem to connect their cats with female sexuality. Delacroix and Gericault like the mini-tiger aspect of cats, typically Romantic, one might say.
As for painting a cat simply because it is loved, then we're not left with a lot.