Despite the game clearly differentiating between sided appendages – for example, one can wear certain items on their left arm or right – it doesn't afford the same attention to using both hands. The only case where handedness matters is with using long or heavy weapons: one must have both arms healthy in order to do so.
Implementing handedness – the differentiation between two hands in using tools or weapons – provides features beneficial to the gameplay and the game feeling.
Sidedness already has precedent in Cataclysm's gear management. Handedness would simply augment this aspect.
The concept of the dominant hand hasn't been explored in Cataclysm yet, despite it's meaningful real-world implications. Using weapons and tools with the opposite hand is less comfortable and will inevitably provide worse results.
This concept ties into the gear sidedness. A left-handed character would find it uncomfortable and, more importantly, time-consuming to reach for a pistol in a holster attached to the right leg. That same character would prefer having a leg-attached ammo pouch on the right side, so that they could reach for it with their opposite hand while holding the firearm in the dominant one.
The same would apply to melee weapons.
Ambidexterity could be added as a trait, starting or trained, to eliminate the disadvantage.
Not always does weapon-handling have to be gracious: sometimes the sheer volume of attack is necessary to bring a tough foe down at close range.
Dual wield doesn't have to be about two of the same kind of weapon. Wielding a pistol in one hand and a knife in the other could afford the combatant the chance they need to survive or at least repel a sudden foe in close-quarters situations. Wielding a short melee weapon and a shield – wielding, not merely wearing – provides obvious protection against having the weapon alone in your hands.
A lot of potential lies with the idea that one could temporarily free up one hand, even when dual-wielding or handling heavy tools, to do something else.
The character could hold their rifle by the handguard while throwing something, like a grenade. They could do the same in order to "flash fire": provide additional fire support with their readily-available sidearm while their main weapon is empty or is ineffective at short range. ("Flash-firing" needn't be a separate mechanic: simply allowing the character to use two hands for two separate items should be enough to enable it.)
In situations where one is required to use a small tool, they could handle the items currently in their hands without permanently dropping them. (This should require using a hand, something that isn't fleshed out in Cataclysm just yet.)