The first time I learned it was from a book by LaMothe in the 90s and it starts with your demonstration of 3D matrix transforms, then goes "ha! gimbal lock" then shows 4D transforms and the extension to projection transforms, and from there you just have an abstraction of your world coordinate transform and your camera transform(s) and most everything else becomes vectors. I think it's probably the best way to teach it, with some 2D work leading into it as you suggest. It also sets up well for how most modern game dev platforms deal with coordinates.

Tricks of the * Game Programming Gurus :)