I thought I made it clear in my initial description that I do not expect the candidate to come up with the "right" answer, and that I definitely didn't come up with the right answer in the given timeframe. Perhaps I didn't make it clear in my post that I am very upfront about those things with the candidate.
Another nice aspect is that the "solution" is contained in a 6 line git diff, and consists of standard "intermediate" level Python/Django. After talking through the problem for a few minutes, getting a sense of their instincts for approaching the problem, I give them the solution we came up with and we talk through that. Their ability to understand the solution is equally important (and not hard... it's a standard diff, standard code, nothing tricky).
To address some of your concerns:
1) The bulk of the context is easily communicated in a dozen or so lines of very standard Python/Django code.
2) Absolutely. That's partly why it's a good question. The candidate and I are acting in those roles (as much as possible, given the setting)
3) Candidates can certainly do that if they want (though for the sake of time, I generally shortcut the answer for them)
4) The circumstances under which I did come up with the solution were similarly stressful, and again, I _didn't_ come up with the solution in the timeframe of an interview, I would be shocked if the candidate did, and they know that going into the conversation.
5) Do you think we're hiring someone specifically to solve a problem we solved a couple years ago...? The question is about critical thinking, approaches to debugging/troubleshooting, collaboration, etc. These are all skills that will be very important for the _next_ unforeseen problem we're going to face.
Talking about similar problems (or problem of a similar scale) that they have faced in their career is generally where the conversation heads next (depending on their experience).
For what it's worth, in my experience it's pretty rare to get feedback from candidates (obviously for different reasons), but this particular question has resulted in several cases of someone reaching out later to speak positively about it.