While I don't know about this exact post, for most academics, such theoretical exercises are their work. 'Projects' like this are nice and small and contained. They also give you the opportunity to get 'real' questions from people who aren't as close to the material as you are, almost like 'customers', so if you use a question like this in a lecture, it's almost sure to capture the interest of students better than other textbook examples. While I don't teach many courses, I've used examples derived from hybrid 'real world' / theoretical questions as examples to explain our products.
That said, I've surely spend time on questions that will never pay themselves back in such a way. You never know up front which ones will, so it's like playing the VC game - you 'invest' in 10 questions, with the knowledge that 7 will be duds, 2 will break even and the last one will (hopefully) be a home run.
First, I am not saying that this is strictly a waste of time. In fact, I do love learning from things like this.
Second, I am not saying we must always be working instead of stopping to try something different. I personally find switching focus very important and I think it's a great tool for a great many people. I find that when people learn something slightly outside of their field they suddenly are hit with a lot of new ideas they did not have before, so learning about random solutions to random problems can be a great way to spend your time.
What I was trying to ask (not assert) was how answers like this come to be. I am somewhat astonished that I can ask pretty much any question on any given subject and a subject matter expert somewhere in the world will then proceed to spend hours putting together a detailed essay or demonstration (or both) of the concepts involved. What I wanted to know is who are these experts, why are they giving their expertise away for Internet Points (tm) and is this detracting from their actual work.
My other question is whether it's possible that at some point the number of soft, open-ended questions on SO will reach a critical mass where most participants will flock to those rather than the specific and hard questions and detailed expert answers that SO became famous for. Clearly we are not there right now, but is it possible and is it going to happen?