The Island question has come up before. See What criteria did people use to delete this question, and should it be applied to other similar questions? where it is #3 on a short list of 4 questions which the poster suspected might also warrant deletion. Notably, the existence of historical locks and their possible applicability was raised in the comments, but none of those questions had it applied: two were left alone, and the other two ended up deleted largely due to that post—including the Island question, which picked up its final 3 deletion votes in the few days following its appearance on the list. Bailey M explains why deletion was proper.
Faced directly with this question, and the choice to do nothing, historical lock it, or delete it, the community made its choice, and I believe it chose correctly.
Not all puzzling questions are puzzles
This particular interview question “works”, if you believe that sort of thing, in that it gives the interviewer a chance to observe how the candidate thinks and approaches problems with no straightforward solution. Indeed there isn’t any particular “right” answer to this question, no hidden clues to find that guide the solver along an intended path, no smaller puzzles to solve along the way. In short, it’s not a scenario designed to elicit a certain solution from a solver crafty enough to reach it, as it isn’t actually designed around any solution at all.
My usual guidance today would say,
Puzzles with no "right" answer are generally discouraged; you should have some objective criteria, even if arbitrary, for determining the "best" or most "right" answer, so that we're not just assembling a collection of valid solutions. Open-ended questions that impose no practical limitations on what kinds of answer will be accepted are, pretty much by definition, Too Broad and very likely to be closed as such.
A historical lock does not seem appropriate
The description for a historical lock says (emphasis added):
An extremely popular question which is now considered inappropriate for the site may be locked for "Historical Significance
It shouldn’t be used for questions which, as here, were never on-topic.
Within 3 hours of being asked this question had already piled up 10 answers. Within 10 more hours, close votes had started coming in. An initial close review failed (3 to 2), but before the question was 36 hours old it had accumulated over 25 answers (of which 3 were promptly deleted by moderators), at least one moderator flag, and enough close votes to close it. Yes, the answers were varied and amusing, but this question was clearly problematic from the beginning.
5 days later, it accumulated enough votes to be reopened.
5 days after that, it accumulated enough close votes to close it once again.
And so it would remain until, many months later, it started drawing deletion votes, eventually accumulating delete votes by 7 site members and a moderator, and was deleted from the site.
In short, it was recognized to be off-topic almost immediately, and handled almost entirely by community members’ votes, not Moderator action.
Mere historicity or entertainment value aren’t sufficient
This very old Meta post asks for an archive to be set up for “legendary” deleted questions — including probably the most legendary question ever posted on Stack Exchange: the (in)famous Boat Programming question, which was—no joke—hard-deleted from the database.
The person petitioning for this archive noted that
[while] most of those contributions don't have "lasting value" in the sense of the law - you can't just throw them away. They contain brilliant ideas, humour, some strokes of genius, and show what rampant creativity and artfulness is present in the programming community.
That argument seems like it applies to our own Island question. And it has a certain appeal; certainly there are amusing answers that it would be fun to share with others.
Having said that, the Boat Programming question remains very much hard deleted, and of the other “legendary” questions that plea sought to bring back to some archive, all but one remain deleted. And despite quite a bit of thought put into what an appropriate archive might look like or how it could be maintained, no official archive has ever been created for this kind of thing.
These questions, our example included, were appropriately closed and deleted. They do not represent good questions, and were never on-topic. Historical locks are a good choice to keep content that was once considered a good fit for a site but has now fallen out of favor as time has passed and rules and community thinking have evolved and refined. That’s not the case here, so using a historical lock to preserve content that was not a good fit even historically seems unwarranted.
But I really want to see it! or share it!
10,000 rep on a site grants visibility to deleted questions. It’s a nice reward for sticking with a site and contributing enough to earn the privilege, and (presumably) by the time one has earned it, one also knows enough about the site to recognize why deleted content was deleted - that is, the “broken windows” effect should no longer affect a 10k user. The danger of letting just anyone see our old broken windows is that less experienced users often do not appreciate why such content is a bad fit here, historical-lock banner notwithstanding, and the last thing we need is someone getting bright ideas from seeing content that was, is, and always will be off topic here.
For those who have earned the privilege of seeing deleted content, there’s generally no objection to taking and sharing screenshots of it; but this should be done with due care, as (again) we don’t want users pointing at deleted content as evidence that their own problematic creations should be fine because people have posted similar things in the past. If you share something, make sure the people you share it with understand that it’s been deleted and why, please.