I do like your idea but that doesn’t mean I didn’t like Stray. I finished the entire game and I loved it. The cat was adorable, the friends I made a long the way were interesting and I really felt for them despite their, uh, limitations. Just leaving it at that to avoid spoilers as I only saw that it was a cute cat game before I tried it and enjoyed being surprised by how it ended up.
But yes, I do think a game like you’re describing would also be fun. Maybe not as a stray cat, per se, but maybe as a small breed of wild cat living away from humans so you don’t have too much interaction with them and they’re something you’re inherently distrustful of.