one idea is that one can simply write and answer such a question
Indeed, the Stack Exchange model clearly allows for this strategy; you're explicitly allowed to write-and-answer your own questions. If they're useful to others, it doesn't particularly matter why you want to do it. There are already checks in place to avoid abuses of this approach (not that I expect any).
I've used the answer-your-own-question strategy myself -- really wanting a good discussion of interpolation that I could point to in answering other questions (it cropped up as an issue in a bunch of posts over the course of a couple of months at one stage), I wrote and answered one on interpolation in statistical tables. In those other questions where I wanted to mention interpolation in my answer, doing justice to the issues would lead to long answers that were distracted by side issues. It's so handy to be able to include a sentence like "On the other hand, if you're working from tables, you can just use interpolation." as part of a discussion of some other issue. That way if the reader doesn't know about it (and I seem to encounter so many people these days who aren't familiar with even the basics) they can at least get some decent coverage at the link (without worrying about link-rot), and I can proceed on the basis that the content of the post is already available, without bothering the significant number of people for which the single sentence mentioning interpolation is sufficient.
As I've come to refer to that question later, I have improved on the original answer I posted a couple of times, though it still lacks an entire subsection I'd like to include.
As a general principle, I think it (answering a tailor-made question to address a specific issue that you want to have a canonical answer on) is an excellent strategy for particular situations.
Such answer-your-own-question exposition on some specific issue style posts are very rare here, so I don't think there's any substantive danger in doing so when you feel the need. The usual mechanisms for encouraging good posts, discouraging bad ones and removing superfluous ones will still function as they should.
Indeed, I'd love to see a few subject matter experts do one or two such posts -- I imagine Xi'an or Dianne Cook or rvl or Rob Hyndman (to name a few such reasonably active experts, hopefully without offending a substantially larger number of other experts that I have not also mentioned for any good reason) could write some great answers to questions that haven't yet been asked in just the right way as to invite a really good exposition on some specific issue within their area of knowledge.
The main downside risk I see is that such questions might be mostly ignored, but the cost is relatively low so it's hardly a great issue.
On the up-side, a very well-written question (and I think my example above perhaps fails on that score) will likely invite other answers. Indeed, the back-and-forth between knowledgeable people in discussing some issues on other questions has in some cases been even more valuable (at least to me) than the answers.
[Indeed, in some circumstances, we could also simply post good questions and see if a comprehensive answer of one's own even proved necessary -- look at some of Jeromy Anglim's questions, for example; he frequently posts questions I am certain he could write quite a good answer to. So that's another arrow in the quiver.]
In short, I think you should simply go ahead and do it where you think it's needed, and not worry about it. You're surely able to judge when the right question for the answer you need to write doesn't yet exist.
Actually, I don't even think the opening paragraph on your question is really required, nor even to identify it as a FAQ (unless people tend to use searches containing 'FAQ', in which case it's potentially quite helpful to keep it).
Either it's a good question or it isn't. Either it's a good answer or it isn't. So if it's a useful question and a useful answer, there's no problem, and no issue (and votes will - albeit noisily - signal opinion on the value). On the other hand, if it isn't useful the system that's in place is designed to deal with that too.
There's simply no reason to hold back from doing what you think will help.