Cobster
Legend
No, not quite. Blizz went through and attempted to normalize all the weapons. So weapon damage still matters, and a slower weapon will increase that weapon damage. But 99% of weapons have all be normalized to have the same speeds. So something like shadowfang, which was slower, got normalized to be the same speed and damage as everything else.
But the few weapons that are slower still affect things. In the 19 bracket, there are 0 slower weapons - so we like to say not to worry about it because things have been normalized as its easier than explaining the full story.
But I think none of the special attacks scale off the weapon damage and it is only the auto-attack that are affected by weapon damage / weapon speed. Even for auto attacks, if a slow weapon hits harder but still has the same average DPS, then surely there is no advantage in having a slow weapon?