My guess is that there is also a rodent problem.
I have to agree with that. If there was no food source, the kitties would move away. And there would certainly be fewer of them. Animals, domestic cats included, will kill offspring to protect sources of food from dwindling.
Archaeologists on Cyprus have excavated the 9,500-year-old remains of a cat (at bottom in top photograph) buried with a human (at top in top photograph) and decorative artifacts. At bottom, the cat skeleton is shown in a plaster shell during excavation.
Top photograph courtesy P. Gérard/Science, bottom photograph courtesy K. Debue/Science