Once you have algebraic data-types in a language, writing a recursive visitor pattern is pretty simple.

Encoding the semantics of a tree traversal operator likewise is difficult in the general case. What exactly would the order be, what if I want to traverse in a non-standard ordering, what about skipping branches; all would be difficult to cleanly represent.

I have seen it done where you return actions with key ones being recurse, stop, replace, and replace & then carry out some function, but again, this is pretty simple to implement.