I'll leave the Falch/Gsword/Gaxe debate for another time, and will focus on the THF balance "defecit" here...
I'll start by saying I'm perfectly OK with TWF and SWF being better ST DPS than THF. I agree that they should be. It's not where THF's niche should be.
As someone pointed out though, cleaves etc. allow the "negatives" of TWF/SWF to be effectively mitigated, which is an indirect nerf to THF by erosion of the distinctive benefit of that THF niche.
Additionally, the ability to stack another set effect and augment on TWF/SWF is a very significant benefit. It's effectively a free bit of gear, which becomes of massive benefit at endgame gear tetris.
When you add these factors together, it seems that something significant is missing in terms of balance. I think the OP has merit in this context, though I'm not so sure on the solution...
I'd propose the following measures to help redress this, instead of simply upping THF damage directly...
1. Make all cleave attacks, with the exception of the initial cleave feet and barb's supreme cleave, restricted to requiring THF. This is a bit of a nerf, but is necessary IMO to allow more distinction between the playstyles.
2. Add an additional red augment slot to all THF weapons.
3. Any THF set items should count as two set pieces towards their given set.
These changes would erode many of the "additional" benefits TWF and SWF enjoy beyond their ST DPS, and also enhance THFs distinctive niche as AOE melee cleave, thus allowing a clear choice to be made.
As it stands, THF is behind the curve across too many aspects to be considered anything other than a sub optimal style IMO.