I always assumed that the jokes were a British thing. And in fact, the writers of Are You Being Served? say as much: that they deliberately set out to make the term sexual. They wanted a single element of Mrs. Slocombe's life that she constantly references to have double-meaning. They could have used anything.
But maybe not. I'm currently reading about the Impressionists. According to the author, in the nineteenth century, cats and women carried an inherently "wink wink, nudge nudge" aura throughout all territory covered by the Impressionists.
With Olympia, Manet used a cat (with a raised tail) rather than a dog. That caused alarm among critics. Renoir, who loved to paint women, women everywhere, raised eyebrows over Sleeping Girl with a Cat not with the fallen sleeve but by having a cat sprawled on the young woman's lap in the first place.
They are coy creatures that seem entirely predictable until they are not. Paglia would posit that the forward leaning "sky"-trajectory male is confounded by (or, in Renoir's case, appreciative of) the earthy "cave-like" secretiveness of the female. In Truth & Consequences by Sarah Madison, the male FBI agent--who is deliberately trying to provoke a pompous male character he dislikes--postulates, "Everything [serial killers] claim to hate about cats, their independence, their 'slyness' is actually a projection of what they don't like about women, instead."
I love my cats but I can't get too sentimental or profound about them, even symbolically. I postulate that my cats in the Farside cartoon would be saying, "Food! Food? Food, food, food. Pet me. Food!"