Since my self-answered question is the most recent example that OP has seen of this, and since I've posted such self-answered questions quite a bit (see here and here and here and here), I figured I should post an answer to at least make my own motivation clear. :)
I'm currently a teaching assistant for a precalculus class that I've been a teaching assistant for a few terms now. Each term, the students have nearly the same troubles with the same exercises, and I end up typing up the same solutions to email to them, or having the same conversation in office hours each term. This seems rather silly. So this term I've been quite a bit more active in using MathSE as a tool to post Q&As that I know my students would benefit from seeing. I realize that most of my more recent posts do not contain interesting questions. They're just exercises, and usually pretty basic ones at that. But they aren't bad questions either. They are questions that people legitimately have, in particular my students, so they certainly are adding the pool of useful content on this site, and certainly aren't doing any harm by existing. So to actually address your question of how to handle such posts: these self-answered questions should be judged by exactly the standard as any other post. If the questions is useful/clear/interesting then upvote it, and if the question is unclear/useless/disrespectful then downvote it. If a answer is good and addresses the question well then upvote it, and if the answer is wrong or doesn't address the question then downvote it.
To address the rep-farming bit, I didn't post any of my self-answered questions to get reputation; it's really just to have some Q&As posted somewhere convenient for me and my students that others might appreciate too. And honestly I'm rather flabbergasted at the voting patterns that I'm seeing on my self-answered posts. When I post such a question, I expect that the question itself will receive no upvotes (they are usually pretty basic questions afterall), but that my answers would receive a couple upvotes since I am making an effort to be thorough and write good solid answers for my students. But then you get cases like this answer of mine receiving 8 upvotes that, really, isn't worth 8 upvotes (originally there was no MathJax in the title of this post and it might have landed on the HNQ as quite a few basic questions do; none of these basic questions belong on the HNQ). And also this basic question that go two upvotes, whereas my answer got nothing. This illustrates how bizarre voting trends on MathSE can be, but I mean, really, this doesn't actually matter.