All interesting!
Wondering ... if the class teacher was suggesting SID by hand, was that so that the unevennes of a beginners stitches would not show? Like the suggestion of doing that, and then a little decorative top stitching.
While I've been piecing for years, I am finally learning to machine quilt. My first SIDs varied, in the seam, on the edge and OOPS, further from the edge.
I now have the SID foot mentioned already. It's kind of like a little plough that follows the seam. On test stitching, I think it will make it much easier, and certainly evener. You need to adjust your needle left/right to get it right into the seam.