They were introduced in the 1800's so that people could go fox hunting!
My dogs often "escort them off the property".
Great! A number of animals have been introduced there that have become a nuisance, eh?
I do think dogs have their uses. Around here where I live everyone has dogs, and everyone has livestock, so the dogs are pretty good when it comes to not messing with animals and birds, but also they do keep the wild animals away. One of my neighbours has the odd problem with ocelots getting her young birds, because she´s right out on the edge of the neighbourhood, right up next to the woods. Her dogs don´t seem to worry too much!
I wouldn't b without my dogs. I have 1 border collie and several kelpies. They help me with all the stock - including the birds.
And you're right about introduced species becoming pests. Both plants and animals.