Looks a lot like the Worst Argument in the World.

Yes. That's a great description! This specific Dark Art is about how to find the suitable noncentral argument quickly; it provides a few general directions where to look.

Clever arguing is the sort of thing we should try to avoid as much as possible.

Depends. But if the goal is to find the truth, then yes.

you aren't going to actually change their mind or have their feelings about you improve.

Well, if you do it right, you are going to influence them. That's exactly why people do it. Of course, if you do it wrong, it may backfire.