The folks who tell you that man domesticated wolves for hunting purposes have not hunted too much.
The truth is that most hunting is not done with dogs for a very simple reason: dogs scare away game.
Most hunting is a stealth performance with hunters hidden in blinds or in stands located up trees.
Dogs to point or retrieve shot birds? A nicety, not a necessity.
Here we see an honest assessment of the needs for dogs when ferreting rabbits. Dogs are emotionally satisfying, and in some locations they can may increase your bag, but nets were invented for a reason.
Here in the U.S., our native rabbits do not go to ground and nest in shallow scrapes in thick grass and brush, so there is no ferreting at all. When dogs are used on rabbits in this country, they are mostly slow-moving beagles used to drive rabbits out of weed-choked water ditches.
What about long dogs and greyhounds? They are sometimes used for hunting hunting western hares which we call Jack Rabbits, a very inefficient sport. which not about pest control at all.
That said, when it comes to terrier work, silence is golden. If you have a single dog that knows its business, and it's a multiple-eye sette that is connected like a race track underground, you are likely to get a bolt and save a bit of digging.
In the hedgerows in which I often dig, bolts are not always possible, as many settes have pipes that, while they may branch, often come to stop ends.
That said, it's always best not to talk, smoke, or bang about too much when approaching a hole.
Let the dog do its job, press the creature in the hole, bay it to a new location, and do it again before rushing in to sink a hole. A bolt may very well be possible, and even if it's not, you may save a bit of digging on an animal which has only been pushed to mid-pipe.