In effect, you could consider many classes of characters as dual wielding when they use a shield. You get defence in return for giving up an extra weapon and gaining whatever offensive capabilities that extra weapon provides, so, naturally, if you swap out that shield for something else then you lose that defence. In a fantasy setting, it isn't asking for too great a suspension of disbelief from the player when you put forth that the difference between using a shield to block or that extra arm supporting a block with a two-handed weapon makes all the difference when a troll slams its club down as opposed to using two one-handed weapons. The mind is willing, but the wrist is limp?
I concur with freakytapir in that it should present access to multiple skills, but only attack once. If you have enemies that are resistant to weapon types, then the dual-wielding character becomes more versatile and useful as a result instead of being relegated to a simple dps machine; however, in a protracted battle, such as a boss fight, that inability to defend really adds up and becomes a hindrance due to the resources required to keep that character alive. This is especially true if both weapons being wielded are equally effective against the boss. It is worth mentioning, though, that perhaps this second weapon is useful in this boss fight as it applies a status effect to this particular boss, but does nothing more after that. I am thinking of the music box in Bloodborne: powerful, but I can get mauled whilst fishing it out of my pocket.
It may then be that, in most cases, the dual wielder is most useful when first entering an area, allowing you to more rapidly gain scope of the enemies' weaknesses before switching to a more focused loadout after discovering that the hatchet is useless in this area. Conversely, this carries a risk because what if you come across an absolute unit of a monster. In these instances, the dual wielder becomes a scout: quick, tricky, and versatile, but quite frail, which is often what we associate with when thinking of such characters. Of course, that is personal perception and may not actually be true.
Just as a little aside, you should absolutely be able to dual wield shields.