Next, nobody is taught how it actually works.
That's true, there does seem to be this assumption that you can remember some secondary school maths, which I guess won't apply to everyone.
Personally I use the wheel because I was taught it for the PPL and can't be arsed either to do the sums by hand with pencil and paper or to find and learn a piece of software that will do it for me. Simply because it's not worth the effort, the wheel takes seconds per flight to do the sums, and it'll take longer than that for the computer to start up!