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

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).