Simply, sometimes there is insufficient detail to determine whether a tree has wood.
Example: post #265856
Further consideration: Wood should only be used when referring to a material, not just a tree by itself. I find it rather unlikely for anyone searching wood to want to find trees. In essence, unless the wooden object is actually used in some form, other than being a natural part of a tree, it shouldn't be tagged as wood. Additionally, have a new tag: tree_trunk, in instances where the trunk can be seen.
Updated