Currently, the most used concept around is that the grab is used to control nage - not just stop him from moving, but through the wrist grab connect to his/her center and bring tori down to the ground.
In normal keiko, I explain to my students, we pretend that tori is so fast in doing the technique that uke did not have tome to pull tori to the ground (although nage stood there for ten seconds trying to figure out what to do...) This way, you get a lot more comitted grabs with full palm of the hand an d which has a clear intent, not just some fingers vaguely holding your wrist. We say that a stiff grab could maybe prevent tori from moving, but this is not interesting. An interesting grab is a grab that can move the person grabbed.
I consider it a useful concept but not "the truth".