So, even though the URL is different, it uses the same cookie? Even if it's the same URL though, I've seen errors because the Tree data has changed, and the previously selected node no longer exists.
I agree that persist should be false by default.
The code to persist selection was added in #14058, but now that you mention it, I don't see a purpose to it either. It was probably added more to remember the last focused node rather than the last selected node, but that's also misguided since Tree.focus() by default does not associate focus with selection.
About PathError, it's natural for set("path", ...) to throw an error / give an exception if the argument is invalid, but if persist:true saves the selection state, probably the error from set("path", ...) should be squelched.
So, I agree with you, and will implement your suggestion.