The thing is, in today's game, Barbs are terrible for new players to try.
Sure they can get to 20 (but honestly, what class can't? And many of them can solo to 20 far easier) but in today's game of BYOH for most runs, being a melee that's completely unable to self heal while using their
main ability is not going to get them into a lot of groups.
And again, a level 20 self healing barb is still not going to have the overall damage mitigation, survivability, and DPS of the 12/6/2 split.
You can (of course) say that the monk splash is overpowered, that the Paladin 2 levels give to much, etc etc, but that's still what you're balancing against.
You don't really need to balance 20 Fighter vis a vis 20 barb, because fighters have the utility of being able to splash with (imo) the two best splash melee classes, Monk and Paladin. They compliment each other very well.
(Monk of course works well with pretty much any class that can splash it).
But again, there's no way that even a Bladeforged 18 barb/2 rogue (for evasion) with the ability to cast reconstruct , or a human (healing amp) with the same and the ability to use Heal scrolls is overpowered compared to other builds.
The game isn't about 20 Fighter vs 20 Barbarian vs 20 whatever any more, the enhancement/ED system has seen to that.
Allowing a player who forgoes more than minimal multiclassing to be able to self heal is not going to overpower the class, nor result in waves of players suddenly making barbs FOTM.
It will allow players (both new and not so new) to have a little more fun, and be able to actually take care of themselves without feeling the need to have another player babysit them.