So, Joe, when does electric guitar get thick?
I think that's what Keith was talking about, the influence of Walter's timbre which, with the help of amplification and his mic technique, took the sound of saxophonists and made it something for guitarists to emulate, not that young Keef heard Little Walter and said, Hey, I wanna play like Charlie Parker! Much of the early Stones is an attempt to capture the sound of records they loved, especially those of the great Chess artists (Muddy, Wolf, Walter, etc.).
And it's a great sound, as was the Sun sound (blues as well as rockabilly; cf. "How Many More Years"), but it's a sound of limitations being turned to advantage. That is, you had the older guys (Wolf & Muddy) taking an acoustic music, Delta blues, and using then-new technology (guitar amps) out of the necessity of being heard at crowded Saturday night fish fries and parties. Once they moved north to Chicago and playing jam-packed clubs the problem became more acute.
The solution: turn it up! Except of course that you didn't have stacks of Marshall amps back then. Turning those little amps and p.a.'s way up meant a new problem: distortion and feedback. Except that... hey, I kinda dig that sound! Do it again, do it again! How do I do it again? SKREEEEE!! Yaaaah! Maybe not like that. But through trial and error people learned the techniques, and new techniques and sounds led to more techniques and sounds and to figuring how to use them, not just to make them.
The same thing happened in the studios when engineers had to figure out how to capture the new sounds, which led to cool effects that couldn't be replicated on stage. So the children of Les Paul heard the sounds and said unto themselves and others, Verily I can recreate that sound, daddy-o, and I will put it in a box that you can step on, and you, too, my children, can go CLANG clang clang. And John Lennon and Keith Richards and Jeff Beck heard the rockin' sounds on tiny radios or record players not much better than a victrola, further distorting the really happenin' but poorly recorded sounds (but IS it really poorly recorded if it sounds great, whether it's "accurate" or not?), and they said, "Oh, man, I want to sound like THAT!" But like the stylized speech of Raymond Chandler's characters or the mobsters in The Godfather those sounds were not sounds found in nature, so when they tried to recreate them they came up with something new and different. (Although the Beach Boys nailed Chuck Berry's guitar to the point where I can't tell if I'm listening to "Roll Over Beethoven" or "Fun, Fun, Fun" until the intro ends. Or is it "School Days" and "Surfin' USA" that throw me? Been a while since I've listened to them.)
Anyway, to answer your question, I'd say 1965 was when the whole thing coalesced. I'd use that Malcolm Gladwell phrase but I'm sick of it. I'll even say that the feedback intro to "I Feel Fine," a no. 1 hit, was the signal that distortion was back and it was a bloody animal. Had Link Wray been able to patent the power chord he'd be a rich man and most of you reading this wouldn't say, Who's Link Wray? Beck's climb up the fretboard in "I'm a Man," where the guitar solo morphs into what's essentially a percussion solo, is another landmark from that period (and also from the upper reaches of the charts.) Ultimately the expansion of the sound palette is the important part, not the dawning of the Guitar God Era. And yes, I'm shuddering as I type that, even though I love lots and lots of Classic Rock and AOR. "Why do you hate classic rock?" I dont hate it. I dont. I dont! I dont hate it! I dont hate it! (That was for you, mi Texas amigo. But you knew that.)
Oh, and it wasn't that Lester wanted to sound like Billie, it's that they both loved Louis. Listen to Pops' trumpet, not his singing (although his vocal timbre opened doors for Billie that might not have opened otherwise), and then listen to Holiday. Direct connection.