There is no evidence that Bach nor Beethoven had perfect pitch.
Oh really? I assuming this is a well researched statement, and based on a decent look at the available evidence.
Lately I've been reading Harold C. Schonberg's The Lives of the Great Composers (3rd ed.). (see
https://en.wikipedia.org/wiki/Harold_C._Schonberg for info about the author). In his chapter on Beethoven, he writes (pg 114)
"Beethoven had absolute pitch, the ability to hear any note or combination of notes and instantly name them; or, on the opposite side, the ability to sing correctly any note without the artificial aid of a piano or tuning fork."
Later on the page he says
"Thus Beethoven with his incredible musical mind, would have no trouble, no more than Bach or Mozart had, writing music guided only by the sounds in his inner ear."
In the back of this book, there are 19 pages worth of references to other books and documents which the author had read as research before he put pen to paper.
I'm wondering how come his discoveries contrast so sharply to yours? You seem adamant that you know what you're talking about.