Are there cases when you would want a w that is not 1 when you are just trying to represent 2D-H?
I think it depends on what step you are in the computations. I think when we get to the visual representation we want the w to be 1, but otherwise in the intermediate steps it isn't necessary.
For affine transformations, the scale of w doesn't matter. When you multiply the two matrices together, the homogeneous coordinate is w. However, with projective transformations (we'll probably cover this later), then the bottom row of the transformation is not [0, 0, 1], so then the homogeneous coordinate is not just w, so then we have to worry about that scale factor a bit.
Alright I see now thanks!