Why is headman's sword inferior to Vaal greatsword in every respect?

I don't get why you claim there would be 3 tiers of each weapon. Is this based on the visuals ? If so, this is a wrong asumption. Sticking to 2h swords, Wraith Sword and Infernal Sword share the same skin but have different implicits.

Sorting by implicits is one way to sort categories that work OK for swords (not so much for axes, as most don't have one). If you do so, you'll see that the Headman's sword/Vaal greatsword skins all share the same, and actually form one group of 6 tiers, from longsword to Vaal greatsword.

Assuming there are 3 tiers of weapons because of visual aspects is not 100% accurate, not only for 2h swords. The game clearly is misguiding though.

I can't help but be slightly amused at all the fuss over an item people don't bother using as a base....