The Wither sword doesn't apply the Wither effect. Is it meant to? Given that it has quite low damage, I would assume that is to balance the intended wither effect.

Using most recent versions of NetherEx and LibraryEx for 1.12.2.

The swords in NetherEx aren't meant to apply any effects. They are meant to do stone sword level damage, but have higher uses, efficiency, and enchantability than a diamond sword.