I think this thread is going away from where you originally intended. Maybe someone will start another thread to address what is being discussed now. Sorry for the hijack.
If you are boxing with someone (unarmed), the common boxing cover is a far better practice than wrist grabbing. The boxing cover allows you to move into range, limits the damage the other fellow can inflict on you, and allows you to land a powerful blow with either hand.
If you want to bring them into a control position (top mount etc) than simply shooting in on them, gaining a double leg or if you miss getting a waist lock or bear hug, than applying a take down into control position is a favorable strategy.
Wrist grabbing, as a non-transitory technique, in an unarmed situation is not the best idea, so there is no real need to train for it. That's why we don't see much training for this in MMA gyms. A wrist grab is only a needed to control the hand specifically, which is seldom needed unless someone is armed.
Boxing. Sure and I have boxing and judo experience. 3 on 1 though. I didn't give anything away until actually attacked.
Control position. Not with 3 on 1.
Wrist grabs. Sure its not a great attack. But if done for real I think it will be a lot more effective than "grab and push to center" or "grab and immobilize". One seminar instructor said something to the effect, that morotedori should be applied as yonkyo.