Since the Hot Network Questions list was revamped 6 months ago, moderators have had the power to remove questions from the list. As Catija, the community manager for the SE network says,
I recommend each site have a meta discussion with guidance for moderators about when - if ever - a question should be removed.
I have noticed our moderation team have been exercising this power (specifically, it always seems to be Asaf Karagila). Most of the choices I agree with, but some I find questionable. So, I think we should outline some guidelines for a question to be removed from the HNQ list.
Specifically, I would like to discuss the following points:
Should an HNQ be removed if the question is not interesting, but it has lead to interesting answers?
Should an HNQ be removed if it is an interesting question, but has not generated interesting answers?
Is a lack of context grounds for removing otherwise interesting questions/answers from the HNQ?
Should we adopt a policy of removing all homework questions from the HNQ?
Given that controversy (which was the cause for the HNQ revamp) is an extremely rare issue for mathematics questions, should we be removing questions from the HNQ at all?
(Added, from discussion below my answer) Should there be any guidelines at all for removing questions from the HNQ?
(Another added question, after discussing with quid) Should we, as a community, care about HNQs at all?