In good old DD, at every 5th level you are entitled to 2 skill points. I don't think you can get to the 5th level in demo.
DD and BD shares one common trait - there's no skill tree to say off, and hence every skill is essential. You will never need to'waste' a skill point on any 'useless' filler skills, unlike in Diablo II. (D2 1.10 sort of solves the problem).
It is not quite 'ridiculous', actually, considering that enchanted weapons usually come with tonnes of bonuses. If the weaponskills are too powerful, then powerful weapons + powerful weaponskills = unbalanced character. 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.
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.
I will try a warrior/warrior combo so that I can explore the warrior class more in depth.