Sword and board came into it's own the better armour got, in cultures with lesser metalworking skills and lighter armours, 2 weapons are far more common. It has more to do with tactics, technology and training (the 3 essential Ts!)
The main reason s&b was more prolific is that it's a damned sight easier to train in, you have a weapon to swing, and a shield to deflect and bash, lovely and simple (trust me, it's REMARKABLY easy to pick up). A 2 weapon fighting style can take years upon years of dedicated study and training to perfect as it's very hard to wield 2 weapons without getting tangled up, but once you can, it's a formidable form of combat.
The best way to get past a shield is by using something like a flail, flanged mace or bearded axe to bash, pin or pull away said shield, so your main attack hits defenceless areas. Try standing on a field in just chain & breast, carrying a longsword and a wooden shield, then see how long you can keep that arm up and defending, then compare it to padding & leather with a sword and axe and I think you'll find a good number of reasons to bet on the 2 weapon fighter.
All this said, you can't just arbitrarily deem one combat style as 'superior' to others in any case.... and even if you did, it would be irrelevant since (as someone already pointed out) this is D&D and therefore so completely removed from reality that my entire above arguement is probably already moot.
Ah well, them's the breaks.