Shoving is a Bonus Action in BG3, so there's no real need for "calculating optimal times" - there is very rarely a better use of a Bonus Action. If someone is near an edge and will take falling damage and be made prone, you can make any other melee attacks on them, then just shove them off the edge. It's also a great opener in any situation which isn't initially hostile where someone is standing near an edge. For example, in Act 1, there's a certain Wizard who likes to look out over a 60ft+ drop, you can just wait for them to do that, hit turn-based mode, Lae'zel or whoever comes up behind them and WHEEEEEEE < THUMP >. I've never seen them survive the fall. Sometimes they go so far before landing it doesn't even initiate combat with the people inside.
Asking "what's the payoff" is a bit like asking "Why melee attack anyone? Why not just use ranged and spells? That way you don't need to stand next to them!". You do huge damage and some CC for a Bonus Action, you waste their time, it's particularly nasty on enemies who only have melee options. More importantly - it's often incredibly funny in a slapstick kind of way, and BG3 is a very slapstick game, combat-wise.
Of course even better than Shoving in a lot of ways, you can bodily pick up and Throw an awful lot of smaller enemies with high STR characters - it uses up one Attack - you can throw them off cliffs, into other enemies (they both take damage), off cliffs on to other enemies (particularly hilarious). I should note Act 2 contains far fewer opportunities for throwing and shoving shenanigans with both than Act 1 or Act 3 for whatever reason.