I cannot claim to understand the extension of energy. While I trained taiji for over a decade, it always was second to my white crane so I never gave it equal focus or attention and perhaps that is why I ultimately never felt I understood it well. I finally walked away from taiji with the decision that it is not a good match for me.
However, I’ve been training the dao for well over a decade, and the jian for not much less than that, both within the context of white crane and taiji. It was immediately apparent that a heavier, more realistically weighted weapon, did wonders for the quality of the training. In short, it does not allow you to cheat on your technique.
A light “boing boing flap flap” weapon often allows you to execute your technique with the strength of the arm and shoulder alone, without the connection of the root and the rest of the body. With a realistic weapon you do not get away with doing it in that way. With a realistic weapon, failure to engage the root and the full body will simply get your arm really tired, really fast. You likely will not even get to the end of your form.
I’ve got some weaponry that could be considered extra-heavy, and this becomes even more true. Sometimes you can barely swing the weapon at all, if you are doing it from the arm and shoulder alone.
This practice translates into empty-hand practice as the rooting and connection lessons are just as important in that context. But with the empty hand, without something heavy in your hand, it is even easier to cheat with your technique, or to even be unaware of the need to root and use body connection altogether. Once you learn these lessons with one weapon, it becomes easy to recognize how it is true with the other weapons as well: spear, staff, double weapons, etc. they all require the engagement of the root and the full body connection, within the context of their particular techniques.
In the modern day, I feel that is where the real value in weapons practice lies. Fantasies of a zombie apocalypse aside, it is just unlikely that any of us will ever need to use our swords and spears in real combat. And, practice with realistic weaponry helps develop a realistic and appropriate and useable physical strength without spending time simply lifting weights, which is an activity that I personally find no interest in.
Perhaps I am saying the same thing as you describe, in different words.