I would argue that this saves both compute and memory for any significant search. In a traditional tree-search without treating states as identical and revistable still requires you to store every node that you visit in memory to track the N, Q, and child relations.

Applying the algorithm adds a hash associated with each node, and a counter on each edge. On the other side you're de-duplicating identical states in your search space, saving the memory of duplicate nodes but more importantly saving compute by not requiring independent searches of the same state space. Whether this trade off actually saves memory will be determined based on how likely duplicate states are in your search space.

Otherwise your summary is absolutely spot on.