Personally I favor what you suggest but with a penalty to the attack roll. Attacking with both weapons, as a single attack-action, 1x/turn, at a -2 sounds about fair. It somewhat balances the fact that you're still keeping your BA free in this, and also allows additional tactical choices.
A big balance issue is rogues vs fighters. Attacking with your off-hand results in a roughly constant additional ~35% damage for rogues (depending on exact level, Dex, weapon, etc), but it results in a range of 45% to only 5%, as you grow in level (sharp drop at lvl 5 when you get Extra Attack), buff to fighters' damage. Great at low levels, but terrible at moderate-to-high levels.
**Numbers may very well be incorrect.
