IRide said it well above. I agree
I don't use any kind of martingale or draw reins while riding, never have on any horse I have owned or trained. They're just not needed in you have enough time and patience to train a horse right.
Now, a friend of mine bought a horse who was a habitual head tosser. He was so bad he'd nearly hit you in the face! His rider used a training fork set very loose, as a safety devise. It only restricted the reins when the horse's nose was nearly pointed at the sky... They kept it on while they worked on his head tossing issue, and eventually weaned him out of it. THAT, IMO, is the only time someone would "need" a training fork.