We're fortunate enough to have an owl (I assume a pair) and a couple of hawk pairs in my neighborhood (I can see them in the nest). There are also snakes (I've had to coerce a 3' black racer off my porch). Rodents have never been an issue.
The problem with denser city living is there isn't a lot of habitat for natural predators.
There's a natural predator in cities whose habitat is "your couch."
But people say that allowing cats to be "outdoor cats" is a bad thing.
(Cats do hunt a bunch of species that aren't going to try to enter your house, and may in fact be endangered. But then... so would owls, hawks, and snakes living in the same areas. My point isn't so much that having cats outdoors is good; but rather that we should apply the same standard to having any of these other predatory species in our neighbourhoods that we do for cats.)
I'm not sure it's actually true that we should apply the same standard to predators who are naturally present in an ecosystem and predators introduced by humans. The natural ones have to some extent demonstrated that they're capable of existing without causing their various forms of prey to go extinct.
Morality aside the uneaten dead birds never go to waste. If a raccoon, opossum, coyote or bird doesn't eat the carcass something else will and it all goes back into the mix. The only way it becomes an actual loss is when a human interferes by putting it in a plastic bag or throwing it out in the trash and dooming it to decompose in a landfill.
cats are not local species, except you live at their original region. cats are invade species, local animals do not evolve with them. cat can easy extinct most small animals in your region, local predators will not. please do not claim "they are same".
The GGP commenter was waxing on about having owls in their neighbourhood to such a degree that you'd expect that they'd be interested in introducing owls into a neighbourhood, as an invasive species, for pest control — the same way farmers traditionally introduced "barn cats" as a pest-control measure.
My point is that any invasively-introduced predatory species can and will end up hunting local wildlife to extinction. A species that has never been invasively introduced before isn't suddenly a more "noble" creature. That's the halo effect. One should treat the statement "we should get a pet owl, and let it roam the neighbourhood freely" with exactly the same suspicion as "we should get a pet cat, and let it roam the neighbourhood freely." There will be an equal environmental impact from both.
(And any predator kept as a pet will hunt "for sport", because you're already feeding them, so any hunting they do — and they will hunt, if for "practice play" if nothing else — will be done on a full stomach.)
The problem with denser city living is there isn't a lot of habitat for natural predators.