Here's a proposal. Even if Blizzard were to allow Dual Wielding 2-handed Weapons (which I doubt they will unless released in an expansion), maybe do something like this.
Grant a passive ability that "Allows the use of 2-handed Swords to be equipped in each hand. All statistics and damage on these weapons is reduced to 60% with your main hand weapon and 40% with your off hand weapon (not including socketed gems)."
Let's say that we put this into action. I randomly selected two 2-handed swords from the Auction House.
The first (main hand) has an overall DPS rating of 1265.1 with 235 str, 257 int, 5.80% Life Steal and 1 Socket.
The Second (off hand) has an overall DPS rating of 1164.8 with 121 str, 184 vit, 160% Crit Damage, 4.80% Life Steal and 1 Socket.
Looking at the main hand weapon first, if you were to take 60% of all the listed values, the stats granted to you would look like this: 759.06 DPS, 141 str, 154 int, 3.48% Life Steal, and 1 socket.
Looking at the off hand weapon, if you were to take 40% of all the listed values, the stats granted to you would look like this: 465.9 DPS, 48 str, 74 vit, 64% Crit Damage, 1.92% Life Steal, and 1 socket.
If you were to look at both items as a whole following this system, the stats granted to you would look like this: 1224.96 DPS, 189 Str, 154 Int, 74 Vit, 64% Crit Damage, 5.40% Life Steal, 2 Sockets.
Add in the normal bonuses for dual wielding, and make some tweaks to the above proposal, and I would say that it can be balanced fairly easily without having to do a complete overhaul of two handed weapons. Would it need tweaking? Of course! But making this happen isn't as extreme as most of the negative comments in this thread are making it out to be.
TL;DR Allow swords only. Add a passive that grants 60% dps and stat contribution from main hand, and 40% dps and stat contribution from offhand while maintaining the full benefit of sockets. You have to give up a passive to do it as well so you'll be missing out on other beneficial passives whether it is damage or mitigation.