"Shove" should stay as bonus action but it's effect should be toned down even more, ...
No, it shouldn't.
Pushing someone (in holes or for other reasons) should not be as common as basic attacks in a RPG. This game is supposed to be a serious one.
Agreed. Shove is supposed to provide a tactical advantage in battle, not be an OP insta-kill option.
They really need to fix Shove. They need to add Shove's most important feature - the ability to knock prone so other party members might get advantage on melee, or when you reach level 5 and your fighters and barbarians get 2 Attacks, they can shove prone as 1 action and get advantage on their second attack.
Shoving 5 feet/1 meter is only an option in 5e that allows someone like a fighter to shove an enemy away from an ally like a wizard so said wizard can retreat 30 feet and still cast a spell without an attack of opportunity being done on them.
But, because Shove is a Bonus, knock prone would be OP at level 5. Shove prone and gain 2 Attacks with advantage? Yeah. OP. So it needs to be an Action. It also needs to have distance reduced so players aren't getting tossed into lava from 30 feet away from the edge.
