Thoroughbred bloodstock gets a lot more vet care than your average horse. I've seen other kinds of mares palpated without a twitch, but I wouldn't do it myself and I wouldn't recommend it. A mare can break a person's arm with her rectum, which is just about the last injury I'd want to have to explain to an E.R. doc. Repro work and breeding are pretty much the only things that the twitch always comes out on. Other vet work, shoes/trimming etc. is always tried first without it, and a twitch or lip chain is resorted to only as a last resort. But when you have 20 or 100 horses to do (and these are not pets, not personal horses, but bloodstock on a breeding farm), sometimes that's what has to be done. Most of the time, a horse that gets twitched for acting up isn't going to get twitched the next time, because the horse isn't going to need it the second time. The broodmares are so used to the twitch that they don't actually care about having it put on.

No major shed will let an owner/manager/etc. make the request to breed a mare without the twitch. It just will not happen.