I've never ever even heard of an interview problem where a b-tree or RB tree was required to solve it.
But my point stands that there are a ton of great little questions that involve very very basic data structures and tree traversal algorithms that you can use to glean quite a lot about a candidate.
You're absolutely right that asking a candidate if they can solve a 2D DP problem isn't telling you anything other than if they'd either seen this problem or they are good at this algorithm. I'm stating that you can learn a lot and eliminate some bad folks by asking some basic coding LC questions.