The only thing I agree with here is removing the bonus action cost to jump.
Bonus action economy requires you to make strategic decisions across the board for most classes, unless you're a Thief Rogue who gets two Bonus actions for some reason. Most things require setup, and the point is to find the best order for the situation. When it comes to Extra attacks and all that jazz, Barbarians fall in line with other Martial classes except Fighter. That's because Fighters are meant to be the crazy multiattack class. That's their thing. Admittedly, Haste has turned that up to 11 by allowing the use of the Extra Attack feature with a Hastened Action, but Barbs benefit from that as well.
The Barbarian Rage mechanic is already really strong, especially if you're a Bear Totem. Even if you aren't and you're a Berserker instead, you still get increased damage while Raging, damage resistance, and the Bonus Action attack. Wanting to remove Bonus Action costs to things just seems silly to me. Yeah, Shove is useful, but it's situational.
Larian has already buffed Berserker to a good place from its 5e counterpart. Barbarians are fine.
