Ike... I'm not sure what you are trying to prove, and you seem to be knowledgeable in the world of cattle and sheep ranching...but your post proves to me you must have gotten your information from wikipedia.
As Mindy said, she saw an episode of Dirty Jobs where Mike Rowe bites the testicles out of a ram lamb...which was implying that if they would show that, they would probably show branding of cattle.
You then, explained to her the process of castrating lambs to her, and said "biting off the sac" would be more time consuming...
You must be confused, as you do not bite off the sac...you don't really bite anything...well I don't think you want to use teeth or bite...I wouldn't want a broken testicle gooing in my mouth. You must cut the sac off first, to get to the testicles.
Ask any old sheep herder, this method of castration was more time effective than the other options. I personally have seen thousands of lambs castrated with the good 'ol "mouth" method...and would put my money on it racing rubber bands or castration tools any day...