Its to easy to explain only 6 types of trees ;-; compared to mining that has 12 ores I believe which is probably why more people mine ore then woodcut 
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There is away we can get people to woodcut more. To do that there must be a reward of some kind at crystal for example: when crafting comes out crystal logs can be used to make a crystal bow/melee/gun/skin etc. Or have a spiky bat that deals a decent amount of damage and is made from spiky logs.
Basically what I'm trying to say is that every wood type should have a use of some sort not just for fire making.