To some extent cats only replaced larger predators, which humans irradiated in the first place. They can be beneficial in controlling numbers of pests such as rats and mice.
As far as keeping cats, indoors, outdoors, not at all, I'm mixed on that. As I said, my parents' cats had negligible impact on the environment, but there are other cats which do. I also know of happy indoor cats. If a cat has only ever known the indoor environment, has plenty of space and toys for mental stimulation, then I don't see the problem. I admit I'm biased, since I was raised with cats.
I'm assuming 'irradiated' should be 'domesticated' as otherwise that seems somewhat cruel?
Yes,
irradiated eradicated. Humans got rid of wolves, bears and greatly reduced the numbers of other predators in the British isles and Ireland.
EDIT:
I meant eradicated, not irradiated. Damn my poor spelling and autocorrect.
Cats as pest control work nicely, that's very true, I've been told just having a cat in the house can dissuade mice from making a home there.
I'm sure there are happy indoor cats but I have a feeling they're a small minority and most cats roam freely, problem is with an 'owned' cat is that they have no need to kill for anything other than entertainment so what tends to happen is the cat either presents the corpse of some small creature it's indiscriminately killed to its owner or, worse IMHO, just leaves the dead or dying prey to be dealt with by someone who has no connection with the cat at all (which is the majority of the 'oh fluffy never kills anything' kind of cat).
Yes, that's the problem. Killing is a survival instinct which gives cats pleasure. It may seem cruel to humans but isn't, as cats completely lack empathy. An animal is only capable of being cruel, if it can understand that it's inflicting pain on another. In the case of my parents' cats, they did kill, but mostly rodents, usually mice which would eat grass seed in the shed. Birds were far too quick to be caught, except for the odd one which was too sick or injured to escape.
I think cats are more of a problem in places were similar sized predators are not native, such as Australia and New Zealand. There's a very good argument for eradicating them there and not allowing people from keeping them outdoors, but I don't think a similar think can be said for the UK and US.