One thing I wish for is for standard library trees to present a way to take advantage of a trees structure, even if they don't directly expose the tree itself. For instance, C++ map could expose a way to start find or e.g., lower_bound from some node. While I'm making a wishlist, I also wish lower_bound worked with reverse iterators (see e g., https://stackoverflow.com/questions/64351187/stdlower-bound-...) :)

I think allowing for starting this kind of search from a given node would cover most (though not all) of what you'd want to expose the trees structure for directly.