That's not just my opinion. That's the opinion over on tvtropes, which is the source for pop-culture tropes. A barbarian class is supposed to deal a lot of damage.
Again, they don't. Please stop.
http://tvtropes.org/pmwiki/pmwiki.php/Main/BarbarianHero
"The Barbarian Hero is the ancient-era (or Future Primitive) badass, armed with muscles upon muscles and a variety of very sharp bladed objects, whose job it is to kill lots of monsters and kick lots of ass."
"His enemy will often be a Sorcerous Overlord: both an overlord for him to be anti-authoritarian against and an Evil Sorcerer for him to be physical and brave against to emphasise the ideal of combined physical and mental mastery. "
So, lots of muscles, job is killing monsters, anti-authoritarian (read: anti-order, chaotic), and brave.
Sounds like 5e hit the nail on the head here.
(and side note: Barbarians do deal a lot of damage. Every Barbarian player I have seen have loved dealing out lots of damage. Only Paladins with their smites outclass them.)
Strength 16 is irrelevant next to the size of the damage die. Power Attack roughly doubles the total damage of the attack. Without Power Attack, the barbarian outputs less damage than the fighter, which is entirely at odds with how these things are supposed to work. The fighter is supposed to be balanced, with the barbarian being more offensively-oriented, and the paladin being the defensive counterpart.
You're just making these things up. I get that this is what you want, but it not being this way by default isn't wrong. There are even optional things in the game called feats that can be used to customize characters.
Turning the barbarian into a defensive powerhouse, with half as many attacks as the fighter and with no way to compensate for that, is entirely the wrong concept!
Well if you only play the game at level 20 then, yes, things will be wonky.
The game is designed around the sweet spot of levels 5-10.
I would think at level 20 the problem would be the full spellcasters not which is better - Fighter or Barbarian.