I have to say that I never ever have heard of a yorkie, that had it's full tail injured/broken.. Legs get injured, and bitches are lost in whelping, but the tail hasn't been a problem.
Well I have witnessed one, but it was a foreign dog in a dogshow, and conveniently it had had it's tail chopped off by a door. Not docked (docked dogs aren't allowed in shows) but amputated. Just the right lenght if it were docked, but nope, it was the door... Yeah right. Docking was allowed then at the country the dog came from.
Mine have their tails and poop is not a problem if you trim the hair on the tail.
And the beauty is in the eye of the beholder. I prefer full tails, I'm used to them.