My question concerns link/cut tree structure after an access operation. I am assuming an implementation with splay trees. As far as I can tell, once you access a node v and splay it to the root, it no longer has a preferred child and therefore no longer has a right sub-tree. Furthermore, you move this tree up to the root of the entire structure, thus the link/cut tree is unbalanced at the root.
My question is about intuition. It seems very counter-intuitive to purposefully unbalance the tree at the root. I understand in the amortised sense, unbalanced trees are perfectly fine but I cannot understand the intuition behind the choice. Is the gain you get from having the most recently accessed item at the root outweigh the fact that you only have 1 child? Is there something else I am misunderstanding? Are there other examples of structures were a counter-intuitive choice is still a benefit?