Well the reason was recently explained in a book by Clint 'Pops' McLaughlin.
Pops explained the the elements of the embouchure need to be added or used in a certain order to get the best result. He has demonstrations and video but the key point was that some things work well in one register but almost not at all in a different register.
Players have always been told to use these elements but we tended to be haphazard about when to use them. There was never any timing involved.
Pops has presented a very interesting idea that is so very obvious that we all should have instantly known it. After all lip compression is commonly known to help high notes but for some strange many players use it in every register.
Pops points out that once a technique is used, then it is used and not available to help us to play higher.
This made so much sense but I had never thought about it before. Almost everything we do in life has a good order and some bad ones. Playing should be no different.
The videos show a very compelling argument about how we need to start paying attention to when we use techniques like tongue arch and lip compression.
There are discussions about this book and Pops' ideas often on the Trumpet Herald Forum.
Learning about air focus means you don't have to waste your strength doing nothing but preventing air leaks.
Using tension or lip compression to prevent air leaks is a severe over-dampening of the lip vibrations and seriously inhibits resonance. Not to mention that people only have so many muscle fibers to contract. Once you contract them all you have nothing left.
It is in our best interest to restrict the use of these until we actually need them for note production.
Pops said that if you blow air all the way across the entire lip surface, then you must use much more facial tension and lip compression than a player who focuses the air to the aperture.
This is an inefficient use of muscle strength and of air as most of both are NOT engaged in actually making sound. They are engaged in NOT making a sound.
Pops has over an hour of video showing how things we use to change pitch have an order to use them. There are 4 things that he places an octave where we should use that technique. It shouldn't happen in other octaves because it does very little to help there.
Overall the ideas presented were unique and exciting.' Pops' website.