Yeah, saving partial search queries would be useless. What I had on my mind was custom search queries, which would take some time to re-create next time. I remember there have been several requests for such feature.
But now I think, as you suggested, it would be better if the user can choose what to save. How about a right-click menu item of "Save the current search results query" when user's right-clicking on the tab header or the node in left navigator? Then MB creates a sub-node with the title of the search query under the node. The user can always access those sub-nodes and remove any if they are no longer needed. Of course, filters and auto-playlists can do the same thing, but this would be a very simple and casual way to save.
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Then, how to replicate one of the previous complex custom searches just with a slight change in query? Click on the saved sub-node. What MB does is re-searching with the exact saved search query. Then if you open the custom search dialog from the magnifying glass icon, you will get the dialog filled with the previous query since MB already remembers the last query for the custom search. Then what's only needed to add is to autofill search box with the search query to help editing when the user clicks on one of the sub-nodes which was not a custom search.