If I am right that the whole purpose of this sequence has to do with friendly AI research,

Luke confirms your guess in the comments section of this post.

then how is it useful to devote so much resources to explaining the basics, instead of trying to figure out how to design, or define mathematically, something that could extrapolate human volition?

I can see a couple of benefits of going over the basics first. One, it lets Luke confirm that his understanding of the basics are correct, and two, it can interest others to work in the same area (or if they are already interested, can help bring them up to the same level as Luke). I would like to see Luke continue this sequence. (Unless of course he already has some good new ideas about FAI, in which case write those down first!)