Why are you so sure that shorthand will provide the same engagement as handwriting, and not closer to that of typing? It seems plausible to me that the difference could mostly be explained by all the superfluous effort of handwriting.
Because writing in cursive/freehand both require planning, planning which is not required by typing. In fact, I will argue that Gregg requires more mental planning and activity than writing in freehand, due to a number of factors about how it is written.