In the past several years of working with multi-channel amps I would agree that there is little difference between leaving them on all the time or triggering an amp as needed. If a multi-zone house audio system is in use, than leaving the amp on all the time ensures quick audio feeds to the rooms in use instead of waiting, sometimes many, seconds for the amp to power on and provide audio.
But, if it is a dedicated theater amp that does not require a quick power up cycle, then by all means tie it into the preprocessor turning on and let it cycle up and down.
In home audio distribution, I leave them on - in theaters, I turn them off.