First off you came across a standard education method of exposing new students to the connection between modes are chords but that is just one ingredient to understanding music. By the way this connection isn't special to Jazz, it exists in classical music too. Not sure how you derived the statement "...were the ultimate key to jazz improvisation and mastery". They are one of many ingredients to understanding Jazz.
The key to mastery is to understand that music is a language like English or Spanish and it has a structure that has evolved. With that evolution "rules" of grammar have also been discovered or imposed on it to quantify what seems to be a standard use. The modes and chords are barely the alphabet. What one need to do is analyze the solos of great masters and see what they are doing, how they speak! Then start inventing your own take on these words and phrases.
It never ceases to amaze me how people push this system, and gravitate to it, as a formulaic method of always playing the right notes.
I've transcribed and picked apart solos by Charlie Parker, Wes Montgomery, Miles, etc. You name it. I'm always amazed and amused that Wes can play every single "wrong" note, every avoid note, the 4th, the major 3rd over a Minor chord, and it sounds cool. He had an ear that was truly gifted. Jazz is a culture. To master it you need to get immersed in the culture, listen to everything from Benny Goodman, Duke Ellington, up through Dizzy, Wes, Pat, Miles, into modern times if you like what people are doing with it, Jazz rock fusion , smooth jazz, or whatever. Learn how every generation copied from the one before. Pay more attention to phrasing rather than streams of notes that chase chords.
As for Blues, you can absolutely solo modally over it. Changing key on every chord, using a different mixolydian with the starting notes on the I, IV and V respectively. Guess who does this? Wes. Most players do not pigeonhole themselves to one approach but apply a mixture of modal, blues scale, and other approaches to building a solo.
Mastery comes from experience and trying to integrate all these approaches. There is no formula for mastery in any form of music, especially Jazz.
I learned Jazz, and guitar in general, is the 70s and 80s. Perhaps this "modal system" is new, or perhaps my teachers didn't buy into it. But I've never heard it called a system. Like I said it is one of many tools in the musician's arsenal and with that it is full of limitations when taken out of context. But when integrated with classical harmony theory, and going through the act of transcribing and analyzing the work of the masters, that one tool gets integrated in your mind with several others. I can honestly say I fully understand this tool, or system, yet when I solo it never enters my mind in the decision making process You could argue that Wes new 100s of volumes of music theory and thought about all of that when soloing, but I'd bet my money on the opposite.
