I don't think shoving can be resolved as an isolated "fix". The entire combat economy needs to be redone to incorporate everything correctly.
You eat an elephant one bite at a time. This is one bite.
Ok, you just ate a leg, the rest of the elephant fell down. Also, as a solutions architect, my career is based on stopping people from fixing things one at a time like rats at a feeder bar taking in issues. Its how you end up with "accidental" or "organic" systems that you now have a system the way it is because a dev team pulled a tetsuo and trapper-keepered in quick hits.
You have to try to see why its like the way it is. Here are some of my theories
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Jump / Disengage as an action. Because you are consistently put into clusterF scenarios with environmental issues, elevation traps, and an *incredibly* ambiguous "threatened" v "in melee and will get an AOO" range. You will die without this mechanic. I have never used jump and never even come close in all of my D&D years playing to come to what I have had to do in this game to date. So if we looked at "fixing" that (not saying this thread is) it wouldnt solve the issue of why it needs to be so heavily used and why changing its economy would make the game extremely difficult.
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Dip. Sure. Only a few things are actually worth wasting a BA on doing that instead of getting a solid hit with a magical weapon, so it should be done prior to battle if possible anyway. Good early game if you find some poison though.
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Shove. Why are you shoving in the first place? That never happens in D&D. We also know Larian loves elevation so they needed a way to take advantage of that. Start a fire, sneak up, shove them off the cliff into it. Or put feather fall on yourself and have a team mate shove you across something. Some fun stuff. But why is it a combat mechanic that is so easily executed when you have jump and disengage. Shove doesnt even knock them prone. Jump is your disengage, this is a combat maneuver and has a 100% success rate on "unsuspecting" (whatever that means) creatures. Its grossly overpowered and you can take most of the encounters and set up a push-centric battle strategy that takes almost no resources, limits your damage, and makes it so they can't close effectively. It is also not based on str for distance.
My theory: I don't have one. it doesn't make any sense. It should be a str based athletics v athletics/Acrobatics contest with a max distance of 10. As someone mentioned, an attack that is a special attack like grapple. Not going to be used very much at that point except ring-out fighting tactics. A nice pocket option, not heavily used by anyone other than fighters and later barbs. I think there is a context missing of why they aren't letting eldritch blast with a push and thunderwave shine. Forget the mage hand thing, its so dumb and turns it into an action once every 3 rounds to keep doing it. Why not let the people with actual force mechanics do the force stuff? What are we gaining by ring-out tactics in this game? It gives a "heh" factor, but I only catch myself doing it if the fight is entirely too difficult. So, if it is going to be an option at all, Im down with it being a type of attack. I get through the game just fine without it and if it went away entirely, wouldn't really care. If they have introduced an issue with it becoming a pushing match like it does in the duergar fight in the underdark, that needs to be solved. I think it would be better served being replaced with grapple and being able to drag people to the edge and drop with checks at the start of every turn.
Hide: Shouldn't be needed by anyone other than rogues. You don't really get a benefit from it other than it breaking aggro. Which is the real problem. They will run across the map to nail a squish even though it puts them into imminent danger from 3 murder monsters. They will do anything to kill that person. Hide automatically removes them from the aggro order. Breaking LOS doesn't make them recalculate, only hiding. Hiding is a band-aid to the larger issue of AI tactic precedence. To me.
Throw/dash/knock out/help - no real issues there. Help expanded to giving someone advantage would be nice. But that is your action in all the cases they have listed
I think there is a larger issue regarding the nature of the combat and the environments you get put into that are making people need it as much as they are. It being a bonus action is good if you need it that much. Making it an action makes sense if it doesnt mean a TPK every other fight. But just doing it based on what it technically would be in the book is merely solving a pedantic gripe.