If you're in an environment where cats are not natural and are invasive

There's no such thing. Cats are a domesticated species, they aren't native to anywhere. Their ancestors were possibly native to the fertile crescent in Syria and to ancient Egypt (among a handful of other places they're believed to possibly have originated from, it's hard to pin down), but even if only people in those places ever owned cats, if they let them outdoors all the time it would still be bad for the environment and cause issues. So instead of expecting something completely unreasonable, like the rest of the world no longer keeping cats as pets, let's stuck with something reasonable, like not letting cats roam freely outdoors.

Keeping cats indoors isn't any more cruel than keeping dogs indoors. You can leash train a cat, or let them out in a cat-proofed back yard, just like we can with dogs. Cat territory size is dependent on availability of resources, they don't have an innate need to wander large distances as a species. Some individuals might have some wander lust sure, but that's what leash training is for. Take them on hikes, you don't have to put them outside unsupervised with the racoons and coyotes and cars and vulnerable bird species.

Outdoor cats have half the lifespan of indoor cats for a reason. The dead cats I regularly see on the side of the highway on my way home from work certainly aren't happier than my neighbour's cat is walking around on a leash alive and healthy. If you learn how to provide proper exercise and enrichment for your cat either indoors or under supervision/on a leash then you don't need to let them outside unsupervised. If you want your cat to be both happy and safe, then there are plenty of options that are better for both your cat and the local ecosystem. This is something we naturally expect of dog owners, there's no reason why we can't do the same with cats.