Also, it's not 'one' weapon, but one 'type' of weapon, hence I believe that SLASHING represents sword-type, which includes daggers, hunter knives, short swords / long swords. CRUSHING most likely represents mace. I have no idea for PIERCING, though. So it is not actually that bad.
You're right.
Slashing: swords, axes, knives, etc.
Crushing: maces, morning stars, flails, frying pans, etc.
Piercing: spears, pikes, tridents, etc. (I did find one in the demo.)
I checked out the full skill tree and noted that Warriors are the only ones who can improve their 'whirlwind' attacks. If the Weapon Specialist skills apply to the Whirlwind skills, then whew, the warrior class is indeed a force to reckon with.
Remember, there are no classes. A wizard can Whirlwind just as effectively as a warrior. But more to the point, you'll want to combine Whirlwind Attack with Weapon Expertise.
