I was a roadie for years for a signed national act that played arenas, the bassist used a single 4x10 and a line out. Band members should be able to converse with each other on stage, which is obviously not an option in the situation described. Your amplifier is there so you can hear it, and you can send a signal to the PA, it is not designed to fill the entire venue from the stage. Ideally people in the first row should not hear your amplifier at all. Stage volume creates hot spots, the goal of the soundman and the PA is to create an even mix for everyone in the venue.
Very good post and 100% accurate.
