Grabbing a wrist or arm doesn’t entirely negate the effects of a shove, nor the possibility of it. A properly timed shove, with a bit of help, can disengage that grip along the way.But the pushing is so easy to be countered. If your opponent grabs on your wrist, his body and your body are connected as one unit, you can't push him back.
This is why in Taiji pushing hand, grabbing is not allowed. The grabbing by itself can destroy all the pushing game.
This is also why ground game can happen in a Judo game. When you throw your opponent, your opponent will drag you down with him.
A: As long as I keep moving back and remain distance, none of your MA technique will work on me.
B: As long as I can grab on you, when you move back, you will pull me into you.
In the following clip, the reason that one can push the other because grabbing is not allowed.
In this clip, one can't push the other back because the grabbing.