The nose ring is pretty much necessary. Bulls (in general and I assume for yaks its the same thing) lose their respect for humans the older they get. It can then happen, that they try to attack a human to demonstrate, that they are stronger (which they are). In this case this nose ring is the only way you can save yourself. Grab the ring, turn it and suddenly a raging bull turns into a quite submissive animal.
I agree that it is morally bad to make another living being feel bad BUT if i have the choice between getting attacked and very likely injured (i dont know the extend but if it stomps on me i guess is could be fatal for me) or have the animal wear a nosering i can pull when worst comes to worst
If you get attacked by a yak or bull with no nosering they can and will easily kill you, or at least injure you quite badly. In this scenario your only way to survive is to aim for the nose, since its the most sensitive part of the body and then get the hell out of there. If you dont have anything close by where the bull can't reach you, you are fucked.