In working on some riddle-rhymes, I had instances of bits of doggerel pop into my head. I found myself thinking, "pity I have no real answer for that. It sounds kind of cool. Very euphonious."
But does that not still fit in with PSE, if stated explicitly?
Another way of explaining what I mean is Lewis Carroll's infamous "How is a raven like a writing desk?"
As near as anyone can say, it had no answer when Carroll first included it in "Alice."
But over time, there have been proposed answers.
"Because Poe wrote on both."
Carroll's own: "Because it is 'nevar' placed with the wrong end in front!"
I would say these answers provide an added dimension to puzzling, even though the original riddle had no answer intended as "correct."