I was actually fine with 4e's flat +1 to damage for having a weapon in the off-hand. I'd actually prefer something like that to this roll twice, do half damage thing.
If they did something like letting you make two attacks, but the damage dice are reduced, say, 2 steps, or 1 step if your off hand is a light weapon, and you only add half a strength bonus or dex bonus, I'd be fine with it.
As it is, I have 3 issues with it as written...
1) it does not encourage the use of a dagger in the off hand over two equal sized weapons
2) the requirement to only use finesse weapons means you're stuck with smaller damage dice already (esp. compared to its otherwise identical feat, rapid shot).
3) Depending on how the division is done, your damage can be reduced by how you figure your damage. Consider, two rapiers, +3 stat bonus. 1d6+3 divided by two round down, the max damage is *8*.
As an alternative, might I suggest...
Dual Wielder
You are trained in using a weapon in either hand.
Effect: when you are using a finesse weapon in either hand, or a dagger or hand axe in the off-hand, and you hit, you may roll the damage dice for both weapons and use whichever one is greater.
You'd lose the ability to attack two targets (I'd design some higher level feat for that), and you wouldn't do more damage than with one weapon, but your average would be a little higher.
Upper level feats: some kind of cleave that allows you to attack more than one opponent with your two weapons, and eventually the ability to use two one-handed, non-finessable weapons.