At one point, tail docking was thought to prevent rabies, strengthen the back, increase the animal's speed... and it also prevented injuries when a dog was working, such as ratting, so a rat could not latch on to the tail. Our modern day Yorkies, most of them anyways, are not "professional" ratters or working dogs. I have no issue with working dogs having a tail docked, actually I have no issue with any dog having a tail docked really. I prefer natural yes, but I have no problem with someone preferring docked either, all preference.
I just don't think "Tail breakage" is a good reason and wish people would just admit it's for aesthetics. My finger can break real easily, should we chop those off too, just to prevent it in case it MIGHT break or need to be amputated? Italian Greyhounds have very thin tails, they are not docked... they could break easily. I am just saying all dogs can break a tail, and if it were that big of an issue, I think ALL dog breeds (except those bred for specific usage of their tail-such as Westies) would have been docked long ago. But they are not.