They're some of the most useless animals in existence, and house cats, which also happen to be a part of this club ("sort of" for the cat)
I get at what you're getting at. Still, I'd like to note that cats only exist in their current form due to how useful they proved to human civilisation and only relatively recently do we have something to replace them with. A replacement which isn't very good environmentally at that.
( and often less permanent )
The problem with cats currently is that they're too good at murdering rodents to the point that they're a danger to (native) wildlife even in cities.
The species that is thought to be the ancestors of current cats were much bigger than our house cats but already mostly preyed on rodents so having them around was beneficial to human settlements. Even to this day less developed countries have cats around on markets to scare of rodents simply by being there. ( as rodents avoid cats like the plague, if they can ) house cats aren't a species that were everywhere to begin with certainly originating from Africa and certainly spread with a helping hand from humans most likely including capturing cats and travelling with them. They were ideal rodent detergents for farmers. Dogs were mostly used to keep other predators away ( protecting livestock and crops ) and protect property during that era. However dogs like wolfs don't actively hunt small rodents such as mice and often ignore most rats as well. Cats however killed these rodents which often damaged crops and ate or defiled stored produce )
One should not underestimate how much influence the existence of cats had on our race. Cat's are natures rodent murdering machines. There's no known predator that's better at slaughtering rodents partially because cats keep killing even when they don't necessarily need to eat. In nature cats have for a ground based mammal surprisingly high success-rates in catching prey compared to most predatory animals. This all is what made them great at keeping storehouses rodent free but also makes them so destructive against the environment )
( Sidenote: Cats are thought to have a negative influence on bird population due to scaring away birds from nests, though we actually struggle to scientifically prove how much of an influence they have as they do reduce the amount of predatory birds in area's as well which normally kill birds. still multiple times area's with cats have proven to have fewer birds around than cats without. )
Of course a house cat inside a house is just a companion animal that statistically reduces chances of getting rodent problems. Dogs also reduce the chance at getting rodents though not by a lot. Companion animals are technically all useless even guard dogs aren't technically worth the investment and they're the best ''investment'' from a usefulness standpoint unless you're getting a price winning greyhound or a showcat/dog to win competitions with, but then... they're not really companion animals anymore.
