And optimization is about figuring out which way you can make a character concept do the most damage, be the best at skills, etc. Seriously, I understand that not everyone cares about optimization, but...
The barbarian is literally designed to use big weapons like the great axe. A berzerker would never want to touch two short swords, even at low levels. A totem barbarian could conceivably pull it off, though there is a diminishing return on the off-hand attack with low dice in light of things like a polearm, which adds the strength bonus to the hit. The class is simply not designed to support two weapons.
The Ranger? We know from recent articles that the Ranger spells are a necessary part of the classes design in terms of damage. TWF uses the same bonus action all those spells do. A Ranger Duelist using a shield and rapier and Hunter Marks will have superior damage and superior AC to someone just relying on TWF. The support for a TWF Ranger just doesn't work.
A Rogue? Any time you want to use two weapons, you are constantly trying to decide if its worth the loss of that turn's Cunning Action. There's too many bonus actions choices from the very beginning. And if you do hit with your main attack, is there a point to using that off-hand attack?
The Fighter is the only class that really can make good use of two weapon fighting, and that's assuming that we're not using War Magic or Bonus Action Maneuvers with any frequency.
So, in the case of two weapon fighting, its not just a case of realizing character concepts. Its that the mechanics in the game make it difficult to actually achieve and execute any concept that involves two weapon fighting since that bonus action is always so busy with other options critical to the concept.
With the way the game is set up, its not a question of "this way does does more damage." Its a question of "can you even do it with the action economy?"
Without GWM, you could make an interesting TWF barbarian around strength.
Let's say your barbarian decides to use a battle axe and hand axes. The bonus from the rage ability stacks with your bonus action attack. If you did a multiclass fighter/ranger and barbarian that liked to fight battle axe and hand axe , you could get damage numbers that look something like this at around level 10 or so:
Two attacks 1d8+8 and 1d6+8 for 36
compared to
Greatsword: Two Attacks: 2d6+8 for 30 damage.
You could have ready access to a thrown weapon all the time. You could make a pretty cool fighter/ranger barbarian totem warrior.
Frenzied not as much. Then again you don't want to use Frenzy too much. That level of fatigue per use is harsh.
I actually might try this with the feat that gives the same benefits as GWM for single-handed weapons. It could be interesting for a barbarian. If I take both TWF mastery feat and Dueling Mastery house rule feat, I could get +1 AC and wield two battle axes. I've always wanted to make a dual battleaxe wielding dwarf.