Agree with your post except this one. Already 1-hit kill alot with shove, it doesent need more damage tbh...
I've seen several "shoves" ending up dealing less damage than a standard weapon attack. If I'm using my action to do something with a lower chance to hit than attacking (as shoving tend to have compared to a weapon swing) I'd expect a better payoff if things work in my favor.
Throwing things in bottomless pits doesn't count. Especially since in that case you are trading off your "ease to kill" with losing the loot that unit is carrying...
Not to mention bottomless pits are pretty damn rare anyway, and they would be even more so if "shoving" would lose its ridiculous current range (once again I'm referring to bodies flying meters away).