If you are running a sheep breeding operation, it's most efficient if you run almost 100% ewes, selling the ram lambs in the fall, and keeping a ram just through the fall breeding season or for a couple of years between replacements.
But wethers can have a purpose on a sheep breeding operation. If you maintain a ram sequestered from the ewes outside of the breeding season to keep a short defined lambing season or for safety reasons (potential aggression), then keeping one or two large skittish wethers are a great help in managing the ram. Choose large wethers so the ram is less likely to try to beat up on the wethers, and skittish so the ram maintains its fear of you since its herd mates are obviously afraid of you.
The other place that a wether is useful is when you wean lambs. Putting a calm wether in with the newly weaned lambs gives them a calm older herd mate who " knows the ropes" and keeps them calm and handle able by providing a calm role model.
In both of these situations try to pick wethers who are leaders rather than followers so that they have a stronger influence on the rest of their herd.
If you are training herding dogs, wethers are better training companions than either small, skittish yearling ewes or breeding age ewes that are either pregnant, with lambs, or have large udders that can be easily injured by young puppy you are training.