The few times I've seen wrists grabbed in ernest the main idea was to block a punch, stop the attacker from hitting someone and then use the wrist grab to hurt the attacker, swinging the attacker into railings, walls, stairs, other attackers or moving into some sort of lock.
I meant serious to resemble my original comments given above. I summarized a couple of past actual violent incidents. One 3 vs 1 mugging and a 2 vs 2 pre mugging. The victims were the ones grabbing and I'm sorry that wasn't clearer. I was trying to point out that the casual idea of the person doing the grabbing being the attacker really didn't make sense.
Ledyard Sensei did a better job of explaining the martial part. From a self defense standpoint unbalancing someone and flinging them into a heap can generate time to get away or to take other appropriate action.