First of all, I am not an expert.
Many moons ago, I had an Adcom ACE-515 Power Enhancer. Everything was plugged into it. When turning it on, it would sequentially turn each piece of equipment on. It started by turning on the
source (analog/CD), then the preamp, and then to the amp. It went in the reverse order when I turned it off. I have made the error of not going in the proper order, on my own, and blown a speaker.
The fact that something has worked consistently does not make it correct. Then again, it doesn't mean that one should change what is working and has been for so long. However, I believe that there is science behind the reasoning for a particular correct sequence.
My understanding is that by turning on equipment prior to the amp being turned on prevents any aberrant signals from being magnified needlessly, which can damage your equipment. The same goes for powering down. Turning off sources and preamps may not be audible to us unless the amp is still on. Why amplify the "pop", which can be damaging, when turning your equipment off? At least, that is how is has been explained to me.
Chacun a son gout!