Jerusalem is overrun by feral cats, so one year they rounded them all up. Next year they were overrun by feral rats.
Now they leave the cats alone.
Not everything in Nature needs to be screwed with.
Where I live no cats. Birds eat them. Yeah I am talking the big birds, falcons, eagles owls.
Rome also has a problem with ferals. The famous “gattis” take care of them. When I was in Rome last, I dropped a few bucks into their coffers.