Consider this: When you use a stunner properly, the animal feels a split second of pain before becoming unconscious. At this point, pretty much every vet would say it can't feel pain.
But if you cut its throat while conscious, it can feel the pain of the wound immediately, and continues to feel it until the brain starts shutting down. This can take minutes. Cutting the throat does not cause immediate unconsciousness, and this is the problem.
Compare a properly stunned animal vs. an animal whose throat has been cut by via sechita, and tell me which one reaches unconsciousness faster. Because that is the animal that endures less pain in death.