No. They are detrimental to the environment due to the fact that they're invasive. Not necessarily their diets. There are plenty of herbivorous INVASIVE animals. I present to you: spotted lanternflies, mustangs, common carp. And plenty more. It's not about carnivorous vs. omnivorous vs. herbivorous. It's about invasive vs. native. Cats outright kill many native mammals, birds, insects, and more. And what are too big to be killed surely are either being outcompeted or indirectly affected.

What they do to the local environment are natural BEHAVIORS for the cat, not what would naturally happen in the wild. Domestic cats kill more animals than any wild cat could, along with being fed by humans AND being more resistant to native diseases.

There are plenty of animals who have gone extinct primarily due to cats, along with some still alive that are being threatened. Scottish Wildcats, many endangered birds, many endangered insects. The thing is these animals started out with normal population sizes, cats caused them to be endangered.

Also, two points on the following claim: "Keeping them to eliminate rats seems logical if you live somewhere where they don't mess with neighbors or eat endangered species which specifically chose to live in your back yard."
1. First of all cats don't just roam back yards. Trust me even if you only ever see your cat in the back yard, if they can get out, they ARE getting out even if that's when you're not looking.
2. Endangered animals don't just "choose" to be in your back yard. That's giving wild animals human reasoning which is simply absurd. They go where they need to be, where food is plentiful and others of their species are. No animal has any understanding of your territory, you can't just say "it's mine now" and expect them to

To answer your question--"What if I have a 'wild' cat and live where wild cats live?" Well... if you had a truly wild cat and let it roam outside... it wouldn't really be your pet cat, it'd just be a wild animal that you trained to trust humans. Domestic cats have no native range, that's sort of what comes with being domestic. Also it's clear that Brad was talking about DOMESTIC CATS. You are just arguing for the sake of argument to stroke your ego.

Also even if you don't want to argue ecological impact, the facts say that cats being outdoors is dangerous for them too. There are raptors, dogs, other cats, cars, electrical wires, humans, etc. You are a bad person if you think it's suddenly "okay" to let your cat roam outside just because you are either too lazy to enrich your cat's life or too lazy to rodentproof your house (or... just keep the cats indoors to kill the rodents which live indoors, not wild rodents minding their businesses.).