The construction is indeed very simple but compared to Vitalik’s construction it does not work for non-membership proofs or proof of insertion, as both of these require to show that a certain leaf is not set, meaning k is not part of the proof and as such it can not be used to resolve the collision of max(h1,h2) & max(h2,h1).
I think membership proofs are not enough if a state transition function can read leaves that are not set yet because in that case a non-membership proof is needed.