Guitar amps and audio amps shouldn't even be in the same conversation.
No need to reinvent the wheel.
"Most guitar players I’ve played with are incessantly fiddling with their pedals to get the sound they’re looking for on a particular song,"
that about sums it up.
"Not sure if a GaN amp could be programmed to mimic the desirable distortion of an overdriven tube amp"
You can get close enough thru a tube stompbox and the cheapest SS amp-after that it's the player.
Guitar amps and audio amps shouldn't even be in the same discussion.