What about the countless cats of the public service being let loose in remote communities ?
They do more harm than most people would care to believe.

//Dogs, on the other hand, can be conspicuous nuisances//

Mate, have you ever heard two cats fighting in your yard at 3am when you're trying to sleep? I'd trade that racket for barking dogs any day.

//Because cats aren't the nuisance or danger roaming stock or dogs are.//

Yeah, when was the last time you heard of a domestic cat mauling someone? They just kill native wildlife and give people toxoplasmosis, which is quite unlikely to kill you unless you have a compromised immune system.

However, there is some evidence that toxo might turn you into a crazy cat lady (or man, I suppose), with an irrational attachment to the horrid little vermin.

//If the wild claims about "dangers" of cats were even remotely true they wouldn't have been kept as close domestic pets for countless millenia.//

The reason cats were kept in the past was because they were useful - they kept down populations of rats and mice, and were effectively working animals. These days we have pest exterminators, so cats are unnecessary. We should ban their sale and breeding. If people want small and annoying pets for company... well, I've got a terrier.

http://www.youtube.com/watch?v=v3Q2HZRjHHQ

We have a bushland reserve near us where feral and domestic cats were constantly being captured. The feral ones were put down and the others sent to the vet for identification (many subsequently returning). Euthanising the ferals took long leather gloves and a steady hand and wounds were inflicted on handlers on more than one occasion.

Last year a lizard and frog survey was conducted using probably the most eminent naturalists in the area. It involved laying roof tiles in grid formations in quite of few likely habitats. After 6 months of monthly inspections only a single lizard was recorded.

Any cats captured in a cage are now quickly taken to the nearest fire fighting water hole and thrown in, possible pet or otherwise. Not fully condoning it but fully understand why they do it.

Real Cat Hypnosis Simulator on the App Store - iTunes - Apple
https://itunes.apple.com/us/app/real-cat-hypnosis-simulator/id1225412864?mt=8

Qld Cyber-wildlife Officers are collecting feral cats and hypnotising them to hunt cane-toads. Both populations are plumetting , lizards are dancing in the streets.

We don't have a cat problem in our quiet court
except at night. The law is that cats are supposed
to be kept indoors at night. Council rules. However
some of our neighbours don't pay any attention to
this - and allow their cats to roam freely. We've
found quite a few dead birds - and it is annoying.
But I'm not sure what can be done about it.