How is it worse than 2H or S&B?
Greatsword is 2d6 + STR + 1.33 (avg) from Great Weapon Fighting
Longsword + Board is 1d8 + STR + 2 from Dueling (also +2AC bonus)
Two shortswords is 2d6 + STR/DEX + STR/DEX from Two-Weapon Fighting with an equivalent of advantage for half the damage.
How offhand attack works right now is weird. Shoot with a bow (or cast a spell), change to two swordswords, run to the nearest enemy and attack with your left hand. Why not with your right hand then? Two-weapon attack is what it is. You make your two attacks in a very short period of time, could say at the same time, or if the first strike kills one victim, you swing around to another enemy and hit them, without first fiddling with whatever you were holding.
It's worse because it takes your Bonus Action. And because it scales worse once Extra Attack comes into the picture. 1d6 is ~3.5 damage on average.
Let's assume level 5 with 18 Str or Dex.
Greatsword is then 4d6 + 8 + 1.33 = 22.33 for 1 Attack Action
Sword'n'board is 2d8 + 8 + 4 = 21 (and 2 AC) for 1 Attack Action
Twin shortswords is 3d6 + 12 = 22.5 for 1 Attack Action and 1 Bonus Action
Dual wielding is a marginal DPS increase (0.17) over using a greatsword in return for giving up your Bonus Action that can only be achieved by Fighters and Rangers. Fighters will eventually get 3 main hand attacks, so they're limiting their potential if they pick dual wielding in any campaign that goes to level 11 or higher and a lot of the good Ranger spells added to 5e (all of which missing in Solasta) use your bonus action, so they're usually better off with greatswords even without the +1.33. They can get +1 AC instead, for example.
Once the casters can start buffing the party with stuff like Haste, dual wielding falls even further behind in usefulness.
This is, of course, ignoring the various feats available in the Player's Handbook. Polearm Master + Sentinel and Great Weapon Master makes dual wielding pretty bad in comparison. Of course, without feats, Dueling while using a shield is overal the best, because losing 1.33-1.5 damage is an insignificant loss of damage compared to the survivability a shield offers.
It's not that dual wielding isn't capable of putting out decent numbers (as long as they don't have to compete with feats), it's that you have to sacrifice your action economy to do so. To make it balanced with the other styles, I would say that it either 1) the off hand attack needs to be a free action if it is dependent on the main hand attack, or 2) the off hand attack needs to be independent from the main hand attack. Otherwise the added damage is too small compared to spending your Bonus Action when the other styles don't have to.
The class that uses dual wielding the best doesn't even get the fighting style; Rogue, whos damage is mostly done through Sneak Attack. Having 2 chances to trigger it is automatically better than having 1, and they're limited to finessable weapons anyway. Trading a d8 (~4.5 avg. dmg.) for a d6 (~3.5 avg. dmg.) is a pretty insignificant loss of DPS compared to simply having a second chance at Sneak Attack, even if you don't end up using your off hand attack all that often.