Probably tag-based filtering would be better than notebook folder/name filtering. But we don't currently have tags.
This replaces my original idea for #2391 incremental search, where search would filter the tree. I agree that you generally want incremental search to be independent, but occasionally you might want to filter the tree by name.
This is only if #2391, #2387, and #2448 all prove really easy and we have time left this year.