Yeah, maybe that instinct is so old, it dates back to human ancestors that still had fur...

Of course, this could also support OP's hypothesis: Maybe there was another set of visual receptors (triggering on cat ears, muzzles or stripes?) that evolved specifically to detect big cats, because they were dangerous predators to us - and we're "mis"using those visual receptors as well now.

I'm not completely convinced: There are other examples of evolved visual receptors against predators that are well-known I think - like spiders. And they do cause a response, but that response is overwhelmingly negative, sometimes so intensely so that it can drive people into a phobia. So it doesn't seem like a negative trigger can flip into a positive one so easily.

Then again, some people have pet spiders and think they are cute, so - who knows...

Edit: Also, maybe the scale plays a role? Spiders are tiny, even the dangerous ones - so a "detector" would have to be highly sensitive, triggering strong responses even for very small stimuli.

In contrast, big cats are big. The detector could afford to be a lot less sensitive, because the scale itself is a feature - so when watching a small housecat, the detector's response could be subdued enough to be "pleasant" in a "spicy food" or "horror movie" sense, especially if you combine it with the already positive response from the "cuteness" detector.

Not sure if this makes any sense, so sorry for rambling...