Istanbul isn't too hot. I think it has more to do with the fact all the buildings in Istanbul are made of concrete.

The city is like a giant concrete pool. No rotting wood buildings for rats to move within the walls of.

>I think it’s more like NYC rats are bigger than cats.

C'mon, man, its a myth. NYC rats are max 2lb. Even the giant rats - those mine sniffing ones in Africa - are 3.3 lb max. A cat is 10lb+ of pure predator muscle and instinct. A rat has no chance against typical street cat (one can see that even from the reaction time perspective - cats with their 20-70ms are among the fastest mammals while rats have only 150ms+. Just watch Youtube cats vs. snakes).

I don't know about Istanbul but the problem is more like, cats are actively controlled in the U.S. in terms of animal control, spaying, neutering, etc. You don't really have a proper predator-prey dynamic play out with the population because the predators are more contained than the prey are.

I have a tiny skinny female 3.5 kg cat who regularly brings home rats that look half her size, my other fat male cat 7.5kg never catches anything nor does my huge 54kg Doberman.

I've seen cats in India choose to hunt only mice shorter than their heads and take their time for the mice to give up all their fight. Cats are risk averse.