For my cats we were lucky enough to live somewhere that had very little traffic at the time, so we'd let the cats out only when we were out.

Then slowly let them out, but only in the garden area, and then only with a leash. Eventually we stopped letting them out. We'd distract them before opening doors.

I don't have personal experience of taking an outdoor cat indoors. It might be worth talking to a cat behaviourist if there's something in particular that's causing trouble.

But based on what I know, I'd imagine outdoor cats have the option to hunt whenever they feel like it, and have the option to be alone whenever they feel like it, and taking those two things away might be the main source of discomfort for an ex-outdoor cat.

It's important that a cat have its needs met, and so in your home there should be secluded/hidden/out of reach places for a cat to go and be in. You likely already have this covered, but the point is to give the cat the option to retreat and disappear from constant company.

Play, which has to replace hunting, is a little different. I keep some hard plastic too large to eat toys out at all times, but these only entertain when my boy is extremely wound up. Most of the time for it to be engaging, he needs to be playing "against" me pretending to be prey with a wand toy or laser pointer. Bouncing balls with their unpredictable movement also work really well, but he will chew and swallow those so the play has to be supervised.

I also keep sticks of matatabi (a plant with the same compounds in it as catnip) for him to chew. They're not toys, but another thing for him to do.

I also never cover the windows completely, just so he can see outside. He likes people-watching. Yet more for him to do.

When he wants to play, he will let me know, there's a certain meow, or he'll stare at me while sitting next to drawer with the toys.

So maybe try playing with your cat instead of letting it outside? Basically addressing the probable cause for it wanting to head out in the first place, which is boredom. Maintain as many things for it to use to kill time as you can, and help with it personally whenever you can be asked.

Also it doesn't take that much. Even outdoors, cats will doze most of time, they sleep several hours more each day than us.

If it seems like your cat doesn't like playing with you, look up videos of people playing with their cat. Every cat has a predators instinct, but the way to entice with play can be extremely varied. Mine goes crazy for the fluffy ball of a wand toy sloowly being pulled behind and corner and going out of sight, (like a mouse or something trying to sneak away) but won't give shit if I just wave it around in front of him.

In my experience, the best ways to modify behaviour have been changing something he wants to do so that it's unpleasant to do (sticky tape on furniture he likes to scratch, setting a metal measuring cup atop the toilet paper so it comes down clattering to the floor if he unrolls it), or distracting with play (making the cat stop what it's doing by starting a play session). A cat doesn't understand punishment, but if you change something so that an obvious consequence that a cat won't like occurs when they do something you want them to stop, they will quickly learn.

We have yards here in the USA.

Most responsible pet owners spay/neuter their pets.

If you bag your dogs poop then you already understand how cats can be invasive.

One dog pooping on the ground is whatever, everyone’s dog is gross.

One cat killing a bird is whatever, everyone’s cats doing it day in day out…. A problem.

The issue primarily is that your cat is the invasive species

You forgot the risks of spreading feline diseases and parasites.

Are you saying outdoor cats in the UK are just as long lived as indoor ones, and don't do any irreparable environmental harm? I don't think the stats will back you on that one.

Which part of all this is supposed to make letting your cat outside seem fine? You basically made list of reasons to keep a cat indoors if you care for its health, but started off with "it's fine if you have a garden" which makes no sense. Unless it's enclosed in a cat-proof way?

Don't listen to them OP. Share your cat with your neighbours.

The difference between a cat and a human is that you can teach the human stuff like, "don't kill birds for fun", or "pick up trash", etc. Humans are shit, but we're smart enough to know when we went too far and stop. Not that we always actually do.

Lets not pretend that every cat owner in New York letting them outside and onto the streets is a good idea. That would be a lot of cats.

It's nice that you can employ cats for their original domesticated purpose, but what does that change? You're a minority among minorities. In most places everyone letting their cats outside would be more like you having a literal thousand of them to take care of pests in the same amount of land that you use whatever amount you have now for.

And even then the cat is still an invasive species, unneutered/unspayed, one too many of them will get you a feral population no local ecology can handle, so stay on top of it.

Such as?

Where in the world, can you let a cat outside unsupervised, and have there be zero chance of it finding a way to kill something, get killed, or catch a disease/parasite?