I've mulled this over a wee bit, and put together some sort of response.
So, the post on Worldbuilding you linked was inspired in part by our
fortnightly no-longer-regular topic challenges, which I originally proposed after reading a similar post on Earth Science Meta, which was in turn based on this suggestion. The Worldbuilding challenges had a pretty good run, about a year or so, and became a pretty big thing; I was quite happy with the success.
After about a year or so, enthusiasm died down, so they're now semi-regular, which has slowly drifted down to pretty much never, which perhaps I should fix. But over that year - and especially in the last few months - I became lass enamored with the whole idea.
See, the challenges made people ask questions, but not questions that they would otherwise have asked. For example, we had a challenge about religion, which ended up taking the Hot Network Questions list by storm for quite some time; it was one of the more popular challenges to that date. But many users - myself included - thought up questions just for the sake of asking questions. That's not good, especially since in hindsight, even though the questions were popular, they were not indicative of what Worldbuilding is about - which is problematic, since they brought a lot of network wide traffic via the HNQ list. I still regret that.
So the first problem is that people will ask questions for the sake of asking questions. That will, I predict, lead to crappier questions, which will likely hurt the site.
I have a second prediction, which is that only the users who are active now will be likely to participate. This wasn't a problem on Worldbuilding; we had (and still have now, to an even greater extent) a very large, active, and committed community. On HSM, we have a smaller community, as evidence by the fact that this question has gotten exactly two votes, four comments, and no answers in between it being asked and me writing this answer.
Let's face it, we're a small site, even by beta site standards. I'm not saying this is bad; as Jack M alluded to, history of science and mathematics is a pretty niche topic. But this means that we have a small userbase, and of that small userbase, not many will be motivated to ask questions for the challenge. An even smaller amount will be motivated to ask really good questions. This will mean that the challenge may be ineffective.
I don't mean to sound overly harsh, but my perspective on how the community interacts on smaller sites has always been a little pessimistic. The third site I moderate, Mythology, is rebooting its version of a challenge, the Myth of the Month. I see the same things happening there, though to a lesser degree than here on HSM. The people who are keenest to do it are those already very active, and those numbers are few and far between.
That's just my two cents, though. We can always try; I don't think that the HNQ will prove a problem as it may have done on Worldbuilding, because the likelihood of an HSM questions making it to the HNQ is much lower - and, to be frank, that may be a good thing.