As a beginner who finished a beginning quilting class only a few weeks ago, I don't know enough yet to say what the class missed.
You asked specifically about a beginning hand-piecing class, and I really wish mine had been a hand-piecing class, but it was all machine piecing and quilting, except that the binding was done by hand. I wish I'd been able to find a longer, more comprehensive class that covered the hand techniques and offered comparisons between hand and machine.
OTOH, for what it was, a 5-session machine-based class where we made a table runner, it was quite good. We learned about color combining, color value, etc. We learned about tying knots, rotary cutting, getting our piece corners to meet at the same place, differences in fabrics and battings, etc.
There were no triangles in our table runners. That's one thing I wish could have been added that isn't as extensive as adding hand techniques.