From your post:
We do know that over a span of 50 + years many practitioners of Bertholy lead side/arm training become stronger in this aspect, and they hit the ball farther and with more accuracy than they previously did. I wonder how much more speed and lag these girls could gain if they did the same?
While many certainly did improve and I find it a good method I find serious fault in your reasoning. These girls have so much lag I would say they almost have too much, not to mention 90+MPH at 13 years old! They have a much better move then you do even though you have been working on Bertholy for a couple of years.
I think you need to realize that none of the top players learned to play using the Bertholy method. So the question becomes "how did they develop such great speed and lag"?
Why can kids do it so well without having to learn it? That is where a large part of the answer lies.
Bertholy created a great method, and was way ahead of his time. There are just many other options available that get the job done.