Perhaps you could have really really heavy melee weapons that could only be dual wielded via power armor. Heck, you could get carried away with a couple of fat boys, and carpet bomb the whole place. Why wield one mini gun or Gatling laser when you can wield two? You could lob two missile launchers over your shoulder, and fire them simultaneously.
Power armor could further augment your dual wielding strength. I can only shoot enemies that are on my level.
The same is true for melee weapons, it would be pretty cool if you could block with both weapons at once. I just got Project Brutality 2.03 for Doom 1 using GZDoom and everything seems to work just fine except I cant look around, I can Jump, crouch, use sights, but cant look up or down, Ive looked around settings and controls and cant find anything. Of course, aiming with two weapons would have reduced range, but it'd boost your firepower. As for blocking and aiming, I personally think that you should be able to attack with both weapons with one mouse button, then aim or block with the other. While stronger characters would dual wield sledge hammers, and assault rifles. Weaker characters could dual wield knives and pistols. In fact, it would add more depth to your strength attribute. Rather it was with guns, or melee weapons. I think dual wielding would fit right in the world of Fallout. You know, when Fallout 4 first came out, found it odd that with Bethesda implementing dual wielding in Skyrim, they didn't implement it in Fallout 4, and it's got me thinking.