Well, since JKR seems to have sort of "skimmed the book" on what real witches and wizards are supposed to be like, then perhaps she has found in her research that, in the Celtic tradition at least, cats are one of the most common "familiars" of witches. They are considered to be supernatural animals, with a deeper understanding of the mystical and spiritual world than other animals, including humans.
The same is true, by the way, of HARES, which are another common familiar of witches (though not as common as cats). They are supposed to be very much in tune with earth energies and the spirit world, and, like cats, they communicate with their witches with an almost superhuman ease. (There are a few other animals that show up more than once as familiars, such as crows and some others, but I'd have to look them up.)
So I'm with you. Crookshanks, Mrs. Norris are "just" cats (and Bao, Nuli and Cyril are "just" hares)
