No, I don't think it's strictly necessary.
Every once in a while we encounter something where the Asker simply misinterpreted something, there was a transient network error, or there was a bug that has since been fixed. Those sorts of questions should be closed.
But sometimes not all variables have been accounted for. A browser add-on that the people who tried to reproduce the error don't have. Or perhaps a country restriction of some sort. Or some other esoteric issue that won't be recognized until someone comes along who had the same thing and found a solution. If the question is closed, that person won't be able to tell the Asker (and the world) what the fix was. That helps nobody.
There's nothing wrong with having "unanswerable" questions. If it never receives an upvote, it'll be automatically deleted in a year (or less).
That said, I think old questions of this nature should get a comment asking if the issue still exists. If not, or there's no response, then it's okay to close.