We won't be keeping these baby boys once they get older. Chances are high that they will sell for meat. Leaving them intact would taint the meat with the nasty characteristic billy goat odor. Also, it wouldn't be very many months before the little buggers would be trying to breed all the females, even their own mother.
Disbudding is required for us to participate in 4-H. There is a human safety concern, but horns can easily get caught in fencing or even locked into other goat horns. I know someone who had two billy goats. They butted heads, as goats do, and tangled up their horns so badly that no one was able to pry them apart. Both animals eventually had to be euthanized.
When horns are caught in fences, it is sometimes necessary to cut the fence to release the animal. Fencing is not cheap and repairs can be time consuming, especially if they happen frequently. Caught horns in fencing have also led to the deaths of goats.
If a young goat is allowed to grow horns, and you later decide the horns must go, they must be either sawed off or surgically removed by cutting down into the skull. There is blood flow into the horns, so sawing can be very nasty and messy.
With surgery, of course you have the added cost of veterinary services. My neighbor purchased an adult billy goat with horns and choose to have them surgically removed since he kept getting snarled up in the fence. The holes the vet cut into the skull became infected. She spent more than a year swabbing out the holes and stuffing medicated bandages down in the openings before they finally healed over.
Disbudding takes about 4-6 seconds per horn and then it's over. In the long run, I believe it's the least traumatic alternative out there. It's the most unpleasant part of raising goats, but it is a necessary evil.