I've watched plenty of engineers explain binary tree traversals on a whiteboard and then freeze five minutes into an unfamiliar tree problem. The gap isn't conceptual. They know what preorder, inorder, and postorder mean. They can sketch a BST. What they can't do is predict, in their head, how the call stack will branch when a recursive function meets a tree's shape.
That's the real skill tree interview problems test. And once you can do it, the patterns stop feeling like 14 separate things to memorise.
TL;DR
Tree problems test whether you can mentally simulate the call stack's shape before writing code.
The six traversal patterns split along one axis: which direction does information flow?
