Disengage in 5e is a bad rule. It's a bad action. It wastes your turn, and you can't even GET AWAY. So, I'm a caster, right? Oh noes, a scary melee mob is up in my face! I guess I'll spend my WHOLE ACTION, doing nothing useful to help the battle, just to move away from this creature. But wait, I can't also Dash, so I'm just moving base movement speed away. On the creature's turn, it can just casually walk right back up to me AND ATTACK. By playing the "Disengage" game, I will never actually be able to attack, and the enemy will still be able to attack me every round. FUN! GOOD DESIGN THERE.
yeah that is on purpose. casters aren't frontline fighters. they are supposed to be squishy. that is their weakness. instead they have to use a spellslot to cast misty step. that is basically a combined dash+disengage all together in one bonus action.
after that they can even cast a cantrip. that is more than fair for casters.
frontline melee characters have high AC, so they don't necessarily need to disengage.
and rogues and monks can disengage as bonus action.
that covers about everything.
Hide is a tricky one, as it isn't really well defined in RAW 5e, when you actually can hide. so i'm all for changes on that, since it isn't possible to implement such a vague description into a video game.
I totally agree on jump+disengage, that they should be seperate, and that jump should just cost movement and no action/bonus action.
On Shove:
I think it should be an action, at least when the other possibility for shove is also implemented.
In 5e you can also shove to get the enemy prone. and that shouldn't take a bonus action. that would be too powerful.
Also, you can considerably increase your shove chances, when they implement expertise, and spells or features to get advantage on that athletics check. A 1lvl rogue/x barbarian is pretty much guaranteed to succeed on such a check.