The place where the weaknesses of 1h cut weapons compared to 1h pierce or blunt weapons really comes out for me is in major Strategus battles, where there will usually be a greater concentration of high level players (30+) in fully heirloomed equipment than in battle. I recently participated in several of them, and the difference between having a +1 or +3 fighting axe vs. having a +0 warhammer or +0 or +1 steel pick was very striking.
In the battle where I had a fighting axe, I had a less than 1:2 kdr. This was not because I fought exceptionally poorly (although it wasn't my best showing...) or because I was not used to the weapon, as I've done the equivalent of several generations with falchions and other short 1h weapons, but because I could hit the other player 5 times and not actually kill him. The worst part though? The enemy army wasn't even in plate. They were in heirloomed surcoats over mail. I can only imagine how much worse it would have been if they had been in churburgs or something.
In the battles where I had warhammers or picks available, I did significantly better. In all of the battles in question, I did better than 2:1 on kdr, and I almost went 4:1 on one of them. I don't think I played that much better or differently compared to the previous example I gave; rather, the main difference was just that I could drop an enemy in 3-4 good hits max instead of needing 6-8 hits from full health.
I'm not sure what, if anything, could be done about this though. Improving cut 1hs would invite complaints from people who only play the game modes where they are perfectly fine, such as normal battle, and doing something about the efficacy of heirloomed armor would also improve the position of 2h and polearm.