Kannik
Legend
Didn't forget. Just figured it was obvious.
Obvious or no, it is enough though to make the difference that makes GWF pull ahead with each extra attack (just as the cumulative +2 to Dueling style also closes the gap, to the point where it ends up dealing more average damage than TWF).
Anyhow, for non-barbarians (or maybe even for some odd barbarian builds...), there are other hidden advantages of going TWF, such as being able to go DEX, which benefits backup ranged attacks, should one be forced to resort to them against far away enemies.
...
Just the fact that there is no to-go combat style, but different styles that accomplish different results, with the simple sword-and-board being the safe solid option for a simple, non-specialized warrior*, while TWF becomes niche, for some agile melee combatants that want more offense, and GW means plainly STR build upping offense in expense of defense makes me feel the rules are actually in the right track.
At least for my part, I was only considering tweaking the TWF style for fighters (and any upper level additional benefits would only be gained if you have fighter levels) precisely to avoid mucking around with the balance and flavour of the other classes. Similarly, it is that this style ends up becoming more and more lackluster over time (plus being extra effective at low levels) that makes it an issue for the Fighter class. The idea of having interesting choices -- which I wholeheartedly agree with with and support -- is diminished when one of the choices becomes less appealing due to its lessor effectiveness.
I have figured out what I would like to do with a TWF.
When you use your bonus action, for each different enemy you attack you may make an additional attack against that enemy with your offhand weapon. This shifts the TWF into scaling really well on groups but leaves single target damage in the Great Weapon domain.
And this would be an idea that does indeed present an interesting option! It increases effectiveness in a way that's quite different in focus than either Dueling or GWF. And, as a bonus, it preserves the different feel of TWF as employed by a Rogue. I like it. Count my vote for developing this variant.

Kannik