Yeah, the amps needed to be big (& multiple) to carry the sound out to the back. The PAs I guess were mostly just vocal PAs, later on with some drums added I guess. I understand the Grateful Dead pushed PA systems forward with their "Wall of Sound" systems in the 70s.
Right, the philosophy was that driving many more smaller speakers at lower watts each gave cleaner sound that a few big ones at higher power.
The "bins" PA speaker system at Woodstock was also pretty innovative, built by an expert tech and were powered with 10 Macintosh amps, for you "gearheads":
http://audiokarma.org/forums/index.php?threads/mcintosh-amplifiers-at-woodstock-1969.404775/
It looks like the Beatles got hold of 100 watt Voxes right around the time of the Hollywood Bowl performance.
At the very least they had "new" Vox Ac50's by July of 64.:
https://en.wikipedia.org/wiki/List_of_the_Beatles'_instruments
I am always amazed at how good some of those live shows sound from the late 60s, with once again very little production. I have seen/heard some concert footage from The Doors and the sound is spot on, very "airy" & 3D. Maybe due to the lack of close miking? Dunno. Or maybe they could just play...
"Airy & 3D", I like that description, almost all my favorite recordings exhibit those characteristics.
I think mike placement(and type) is the single most single most critical element when recording live performance, and even in the studio for that matter.
A good engineer knows how to mike a variety of studio environments to achieve good "presence".
One of Page's tricks for example was mic'ing his AC30 very close to the cone at a relatively low volume.
Also used by Beatles' engineer Geoff Emerick and examples noted in that Wiki link above.
"Live at Leeds" is another with excellent presence, recorded right around the same period as Quantum Strummer mentions.
Dan Healy, the Dead's "sound guy" always mixed from a spot close to front and center and that's where "the taping section" usually was too.
But the PA was mic'd from the stage.