Here are somethings I have been wondering about for years.
When a band plays an arena or a stadium, are the guitar players and the base player still playing on their own little on-stage amps which are then picked up with microphones a few feet in front of each amp? Presumably then the signals go to the main mixing console to then go to the main PA system. If this is indeed true is this done to allow the individual players to personalize their sound by adjusting their guitar controls/pedals and their on-stage amp settings?
Or am I totally wrong, and the guitar signals go out to the main mixing console and then everything is handled from there?
The first of those - the amps have mics in front of them which capture the sound and send it to the PA.
In terms of whether there’s a “battle” between the Stones amp volume and the front of house mix - in the size of venues the Stones play, it’s not really an issue. An arena/stadium PA can comfortably obliterate the mightiest of amps.
There have been a myriad of attempts to do something different over the years, from various digital amp emulators (which are just about starting to sound realistic, but it’s been a long bumpy road), to attenuators (which take some of the amp signal and convert it to heat before it hits the speaker, allowing the sound of the amp to stay at full blast without the volume), to more moderate ideas like keeping all the amps at the back of the stage facing away from the crowd (Green Day does this - any “amps” you see facing forward in their stage set are just props).