When I think about dual-wielding ... I think about criminals and rogues, people who rely on quick and discrete attacks on unsuspecting people.
While not practical in the Robin hood sense, a medieval alley-robber would be a man or woman who has a small, concealed dagger - or two. It's practical if the criminal has to ambush two people who are in company - or, more realistically, sneak up and threaten a man with a knife at his throat.. while the other knife cuts his purse clean off his belt.
Other than that .. I can only think of dual-wielding as a sort of backup weapon. A samurai might find himself in a tight spot where he has to draw his wakisashi to ensure an escape. Why the Japanese didn't use shields is beyond me...
The Japanese most often held their katanas with both hands, and the schools that trained in dual-weilding with those wakizashis were so rare as to be more legends than fact.
As for the first part of this post...
Methinks you might have gotten your notion of dual-weilding from D&D. Just as a little parable for dual-weilding lunge attacks that are just as powerful and accurate and take no longer than regular attacks without doing something stupid like diving forward and landing prone, let me compare this to something else in D&D: Rangers (or anyone willing to spend the feats) get a bow attack where they put multiple arrows on the same bowstring, and fire them all at once. Yes, up to 4 arrows, all put on the same bowstring firing all at once, with no reduction in damage.
Too bad that completely breaks all notion of conservation of energy, as the same force in that bowstring being pulled back that would be applied to just one arrow is now being divided between four arrows, meaning you just launched four arrows, each of which have 1/4 the energy and speed, and likely none of the accuracy. That's even assuming you could pull a bowstring back while holding onto 4 arrows at the same time. It's pure munchkin mechanics.
Swinging a weapon is a full-body activity. It's not just the weapon that moves, or even the arm. To be a proper strike, the rest of the body has to move with it. This means that to swing both weapons at the same time, you either have to do some foolish forward lunge that largely amounts to leaping forward, and trying to fall onto your enemy, weapons-first, (which, again, leaves you absurdly vulnerable if it doesn't kill your enemy, and such an attack would be highly graceless,) or to be a clapping-like motion that would first require completley exposing yourself to pre-emptive attack, and not allow you to reach forward any. Even then, the clapping attack still isn't going to be able to attack with full power, much less full accuracy.