I've always thought of that question as being more about the nature of identity itself.

If you lost your memories, would you still be the same being? If you compare a brain at two different points in time, is their 'identity' a continuum, or is it the type of quantity where there is a single agreed definition of "same" versus "not the same"?

See: 157. Similarity Clusters 158. Typicality and Asymmetrical Similarity 159. The Cluster Structure of Thingspace

Though I agree that the answer to a question that's most fundamentally true (or of interest to a philosopher), isn't necessarily going to be the answer that is most helpful in all circumstances.