Human feeding of cats can increase their population far above the predator-prey limits that existed for millions of years. As they say in ecology: "What you feed succeeds."
All felines aren't exactly interchangeable either. Domestic housecats are naturally extant only in the Middle East, but everywhere else they have been introduced by humans.
> Domestic housecats are naturally extant only in the Middle East
That's not really true - in most of europe, the native wild cats and domestic housecats are closely related and interbreed. see e.g., https://en.wikipedia.org/wiki/European_wildcat (Iberian Peninsula, Italy, Central and Eastern Europe to the Caucasus).
Many of the types of domestic cat found across europe were already bred in antiquity as well.
So it's not that clear-cut, and local wildlife has adapted quite well to it.
All felines aren't exactly interchangeable either. Domestic housecats are naturally extant only in the Middle East, but everywhere else they have been introduced by humans.