The shape of the letters is largely irrelevant, the source of motion is the important part. In regular cursive it is the fingers that move the pen. In business penmanship it is the shoulder that moves the hand which is incidentally holding a pen.

Here is a video that gets most of the basics right: https://www.youtube.com/watch?v=9TWpFsv9Ib0

Here is one that gets it wrong: https://www.youtube.com/shorts/vCPPcweLKWQ

The reason why the letters have the shape they do in business penmanship is for legibility and ease of motion. There are several variants of most letters you can choose from. The standard alphabet as given in that book is a very good compromise. The reason why newer cursive hands that use finger movement have a lot of the same shapes as business penmanship is cargo-culting.