It sounds as if the problems here are more the facts that Shove has a ridiculous shoving distance and that it only costs a Bonus Action.
Ideally we would remove difficult terrain in the first place. I always found this a bad gimmic. You should be playing smart, not using difficult terrain to cover for sloppy position and poor decisions [yes not everyone uses it this way. But I find it is used to easily as a cheat card]
In 5E, there are legitimate, RAW, no-homebrew-needed shenanigans to set up difficult terrain and exploit it. (Incidentally, the Dungeon Dudes made
a video about this recently.)
Just like summoning an army of creatures to fight for you, I feel this is a legitimate style of play. (Of course, you probably won't summon a super large army in 5E, as I think most summoning spells require Concentration. But unlike in BG3, you can have more than one summoned creature.)
