I personally don't like the idea of using dogs to hunt foxes, however I do realise that something has to be done to get fox numbers back under control.
Are foxes that much of a menace and are their numbers that out of control? In the past I've used dogs for hunting rat and rabbits, because it's quicker than shooting. A team of dogs can do in an hour what would take a gun all day to do. With large rat infestations, a team of terriers can kill hundreds of rats in a few hours. A job that would take a gun days or weeks to do. And it avoids the use of poison which goes back into the food chain endangering things like birds of prey.
I've never heard of foxes being that much of a menace apart from pinching the odd bit of poultry from a shed or coupe.