Greetings,
I feel that the Carpenter's Shop and the Wooden version of it should have more skills and patterns you should be able to make out of it. The same could be said for the Workbench. I feel it should be able to perform Carpentry actions as well as at least Bowcraft.
I also feel you should be able to construct furniture from it, but understand that the current method at the moment for furniture construction requires you to construct a furniture pattern down on the ground first. Personally I feel this goes against the flow of the other crafts in the game. Maybe add in the 20% Carpentry bonus to all cells adjacent to the Carpenter's Shop, making any furniture built near it have the 20% Quality bonus. That could be a bit of a work around.