Actually it should as a naturally-generated wood.Pearlwood shouldn't even have them
Nah spooky moon is a post-plantera event.The question actually is, why should they exist?
The spooky wood is acquired in the end game event, the Pumpkin Moon. One in their right mind wouldn't ditch their equipments to use weapons and tools of Spooky Wood (If they actually are related to the other wood crafted weapons and tools). The set isn't even good for summoner, since there are better summoner sets at the moment you acquire it.