I must say I do not agree with you.
I am with my 15/21 awesome/awful hybrid build and I have been using stabless 1hers for a long time, since I prefer the cleaver/maces/picks.
The right swing is awesome, I'd say even better than the left one, at least with my playstyle. I dont facehug, I stay just out of reach and then quickly get in reach, rightswing to the face, and back out, minimising the damage received by my shield (only 4 shield skill atm). I have often killed people in EU3 just by using this, or at least hit them 3-4 times before getting 1hit by them.
The left swing, nice as well. Fast and headseeker.
Overheads, the only bad thing about them is when you mess it up (i blame most of mine on my 100+ ping though), but its not a problem of the animations. With better ping I would use it much more often, since it contacts almost immediately and rarely glances.
About stabs, I'm really not an expert, haven't used stabby weapons in a few gens, but today I tried specifically the warhammer/italian just to check this. The warhammer stab is just not worth it (low damage, no KD), but nice sometimes, but on the italian its so damn good. What bjord said works often, facehugging works, you just have to position yourself right (should be easy with 9/10 athl).