Jean Lemmerman once told me that the handlers at NOBA preferred a bull to have horns that had been shortened rather than removed.  They claimed that the horns had saved a few of them by making the bull's head too wide to crush the handler into a corner, or in one case, the gutter after the handler took a dive.  They also claimed that the horns gave one last chance to use as a handle to try to push away from the bull if he charged.  Their facilities were first rate; extremely heavy pipe fences and a policy that the handler was always on one side of the fence and the bull on the other as they moved from the stalls to the collection arena, but close calls still happened once in awhile.