There's nothing wrong with a DEX-based barbarian build. After all, rage works as long as you attack, it doesn't specify it has to be melee. A DEX-based barbarian will have a better unarmored defense, can still do good damage, etc. The damage resistance from raging it then the important part, not the damage bonus from raging, and if you go the typical totem warrior, it is nearly universally applicable.
I can't say I agree that the damage bonus is pointless. Sure, it isn't
huge, but it's absolutely supposed to be the Barbarian's equivalent of Superiority Dice or Improved Critical. And since it is a flat bonus, it's much easier to factor into any damage calculations; assuming equivalent hit rates (note that this is
not true, but I'll get to that in a moment), +2 average damage per swing is equivalent to raising your die type by two stages (e.g. gong from d4 to d8 takes your average damage from 2.5 to 4.5). Rage
starts off being better than trading up from a long sword to a greataxe (1d8/4.5 to 1d12/6.5), and ends (at level 16) being better than trading from a dagger to a greataxe (1d4/2.5 to 1d12/6.5.) Or, if you prefer, it gives you 20% to 40% of the benefit of all those feats DMs love to gripe about like Sharpshooter or Great Weapon Master, with
zero of the downsides. Or, expressed in average combat rounds expected per day (about 25), since starting at 5th level you make 2 attacks a round, so that's 50 bonus damage (times your hit rate, of course) over the course of the day, vs. a 5th-level Battle Master's 4d8 (average 18) bonus damage per short rest--which will typically mean ~36 or ~54 damage a day.
However, the more pertinent issue here is
Reckless Attack, which gives advantage on all attacks
made using Strength (though with the caveat of granting it to all opponents.) +2 damage
and Advantage on attack rolls is the real draw of the class, and the reason why you get all that juicy damage mitigation. (Overall, you'll expect to take less than twice as many hits if enemies have advantage, so taking half damage from physical sources is more-or-less cancelling out the Resistance offered by Rage; Totem Barbarians are desirable because their expanded resistance covers all the other stuff usually inflicted by
magic as well as by mundane weapons.) So, not only are you hitting harder, you're also hitting and critting more too, but only with Strength attacks. You give up an awful lot by trying to be a pure-Dex Barb. Circling back to the Battle Master comparison, Reckless Attack raises your hit rate from (to use the typical average) 60% to 84%. Those 24 extra percentage points will be
highly noticeable--not to mention the increased critical hits, which your other Barbarian class damage feature (Brutal Critical) is designed to exploit.
Though really, there's an easier and simpler way to show how and why the Strength stuff actually matters. Go ask if people would be okay with letting Rage and Reckless Attack apply to Dex-based attacks, even if it costs a feat or the like. I have.* People will instantly tell you that that would be stupidly broken and overpowered, utterly unacceptable, never appropriate for any game ever. If it would be stupidly broken to let it apply to Dex, you are
at the very least giving up powerful features by ignoring Strength.
*Had been trying to find a reasonable adaptation of the 4e Avenger in 5e, and Zealot Barb actually fits shockingly well....
if its features are allowed to work with Dex, ideally using heavy weapons with Dex as well, because that is essentially their whole shtick. Robe-wearing holy warriors defended By Faith Alone (stupidly high AC for cloth) who wielded massive fark-off greatswords or executioner's axes with uncanny precision (Dex). Refluff Rage as "Oath of Enmity"--maybe restrict the damage/RA bonuses to just your chosen Oath target?--and you're done, that's a 4e Avenger using 5e mechanics.
However, then you are not tanking with that character, which depending on the rest of the party, could become a problem. But, take something like crossbow expert so you can put the build right in the middle of the fight, and then you are tanking as well.
It isn't the "typical" approach to the barbarian class, but then again neither is the STR-based sword & board ranger, which is a PC I am currently playing and having a lot of fun with. He even stealths.
"You can do it" and even "you can have fun with it" are not the same as "you are making significant sacrifices to do it." Just because it can be played, or even can succeed, has no bearing on whether you're paying a steep price for meager benefit.
