Fighting With Two Weapons Improves Defense Not Offense

A D&D/d20 mechanic that is all-but-universal is some kind of attack improvement when wielding a weapon in each hand.

I find that to be the complete opposite of the primary—and, in my opinion, obvious—reason for the choice: giving you something else to parry/deflect enemy attacks with. I see no benefit to you when attacking; if you make an attack with the off-hand weapon, you are going to be parrying with the main-. A momentary swap, not an addition.

There is no functional difference between sword-and-dagger and sword-and-shield. That swap likewise works with a shield; I bash or swat you with my shield, but my weapon’s role becomes protection for that moment.

A modern D&D mechanic I agree with is the +2 defense bonus granted by a shield. This leaves space to grant a +1 defense bonus to an off-hand weapon. The difference being size of my off-hand tool.