For me it is a matter of comfort and I like the sound of a Strat better, but I do have an LP Classic. I just never can get comfortable with the LP. I have one Strat that is as heavy as most Pauls, I put CS 54s in it and it is wonderful. My other Strat is an American Deluxe with the soft "V" neck profile and S1 switching. It is very versatile for me. I use a BOSS Bass EQ pedal with Fender amps and it makes both the amps and the guitars sound better, removes all the flub. Did you forget that Jimi used a Strat mostly, though he did use Gibsons too, David Gilmour, Pete now plays a Strat and sounds like he always did.
One thing may be QC of Les Pauls. One is a gem and another is a boat anchor. The Peter Green/Gary Moore LP is an awesome guitar. Kossoff got great tone (he also only used bottom cabs for his tone. Mike Bloomfield... anyway that is my theory, weight/QC/comfort.
I imagine Clapton switched after seeing Jimi play and having his LP (Eric's) stolen.
I've never had a decent SG but I think I would like it, though I prefer a 25.5" scale... it is just what I am used to.
As far as the music you have to consider that it was all new in the late 60s and early 70s. They were re-doing all the blues tunes as blues rock and everything was new. These days it is hard to come up with anything new in that classic rock style of music... it was easy then because it was all new.
IMO.