Chaosmancer
Legend
I'll add another houserule we've been using which helps Fighters in such situations, another of @DND_Reborn's work:
Action Surge can be used to multiple the lifting and jumping capabilities of the PC by a factor equal to the proficiency bonus.
So, your PC can lift 420 lbs at level 1? Spend your Action Surge and it doubles to 840. At level 5, it triples, and level 9, it quadruples, etc.
Your PC can jump 18 feet with their STR 18? Spend your Action Surge and it doubles to 36, then goes to 48, etc.
This way, a Fighter anyway, can perform superhuman (IRL) but plausible actions in a fantasy game.
Ooooh, I like that.
It wouldn't be hard to expand this to allow Rage to perform similarly. But I don't know if I could as easily see it going to other martials. Monks have Step of the Wind, a Rogue using Cunning Action might be able to jump further maybe?
Monk jumping and mobility is pretty decent right now, I could see letting players spend ki for boosts. Since Rage is longer, I could see them just doubling the numbers, though maybe eventually give them a little more speed. Rogue is tricky. I think rogue mobility with cunning action is generally decent. They are much more urban sprawl specced in my head, so just giving the climb speed fits my conception of them pretty solidly.
Also, another idea I've been thinking of is a modification to Rage. Instead of the way it works, what if Rage increased the Barbarian's Strength by your proficiency bonus???
In levels 1-4, it would be a +1 to Strength-based attacks and damage, instead of just +2 damage. Of ocurse a +1 to Strength checks is not as good as advantage, it helps a bit.
The accuracy aspect is a bit of a problem for me there. Running numbers Yeah, it should be fine, as long as the Barbarian doesn't get a weapon with a modifier. With the 30 strength giving a +16 to hit, they already rarely need to roll to hit anything. It that gets much higher, then it becomes pretty much pointless to roll attacks, you'll just hit.
Other than worrying about accuracy, I do like the idea.
However, look at what becomes possible IF you ever got to level 20? You have unlimited rages, and with Primal Champion could have a Strength 24, bumped up to 30 while raging!!! Time for some fun working the numbers:
Str 30 x 30 = 900 lbs, go Goliath => 1800, go Bear Totem => 3600, allow Rage to multiple lift / jump like Action Sure, and now you have 21600 lbs-- over 10 tons. I think such a system which is build for such power, in a fantasy game and at level 20, while most definitely superhuman, would be acceptable to many groups.
Jump back to level 1. Str 20 x 30 = 600 lbs, Goliath is 1200, Rage x2 would make it 2400 lbs, roughly twice the real-world limit for humans currently. Since this is a raging Goliath barbarian, is that too much of a stretch at level 1? Not IMO.
I like it.