Well if we just went by gut instinct then apparently two weapon fighting is fine. But the math says something very different.
So far I have just looked at the Fighter, but now I want to look at the Ranger, which is the only other class that gets the Two Weapon Fighter fighting style...
The Ranger doesn't get Great Weapon Fighting, but they do get Dueling, so other than that they are the same as the Fighter at 1st and 5th level. At 11th level the Hunter would get Whirlwind Attack (assuming a melee two weapon Ranger here). The Beast Master just has his pet getting more attacks, so I'll just focus on the Hunter.
The other "ability" is Hunter's Mark. And I really question considering it as a primary Ranger ability since it isn't even included in the OGL rules. But it's all we got, so I'll go with it.
1st level
1h weapon: ~9.5 damage
2 weapons: ~13 damage
1st level, casting Hunter's Mark
1h weapon: ~13 damage
2 weapons: ~10 damage
1st level, with Hunter's Mark up
1h weapon: ~13 damage
2 weapons: ~20 damage
I'm sure this has been covered elsewhere before, but the two weapon Ranger takes a hit in damage when he casts Hunter's Mark, and he doesn't make it up until the 2nd round on the same target.
5th level
1h weapon: ~21 damage
2 weapons: ~22.5 damage
5th level, casting Hunter's Mark
1h weapon: ~28 damage
2 weapons: ~22 damage
5th level, with Hunter's Mark up
1h weapon: ~28 damage
2 weapons: ~33 damage
Here at least the two weapon fighter doesn't lose damage when he casts the spell, so he starts getting the extra damage on the second round, but it takes till the 3rd round on the same target before he surpasses the 1h weapon user.
11th level, Whirlwind Attack (I'm going to be generous and give them 3 targets)
1h weapon: ~34.5 damage
2 weapons: ~25.5 damage
11th level, Whirlwind Attack, casting Hunter's Mark
1h weapon: ~38 damage
2 weapons: ~29 damage
11th level, Whirlwind Attack, with Hunter's Mark up
1h weapon: ~38 damage
2 weapons: ~29 damage
Hunter's Mark really isn't very useful for Whirlwind Attack. Only one target takes the bonus damage. And it sucks for the two weapon user as all of their attacks are with a light weapon and doesn't benefit from the Duelist +2 damage bonus. So the more targets, the further behind they get.
Before anyone starts going into how the two weapon Ranger can start pouring the damage on after the 2nd round of combat, consider the odds that his opponent will even still be standing after 2 rounds, let alone 3.
There is also the consideration of the Concentration save. Every time the Ranger takes damage there is approximately a 35% chance that he will lose the spell (assuming a +2 Con bonus vs. a DC 10 save). There is actually a pretty good chance that the Ranger will lose the spell after the first round of combat. He will then have used a 1st level spell slot so that he could do less damage for 1 round. Yay?
And every time he has to change targets, he actually reduces the amount of damage he is dealing. So yeah, I'm still okay with my house rule.