From the standpoint of safety, longevity and energy savings, it makes sense to power down everything. This is particularly true of tube gear. I can understand not wanting to power down amps which can take a really long time to come back up to song, but, these are exposed to the most heat from being left on, and these can do damage to speakers if something happens while you are not there to power them down. As for thermal cycling, that is really not an issue because it happens relatively slowly. If you look at rating of most parts, they include rating by operating temperature--the higher the temperature the shorter the life.
I only keep on what is meant to be on all the time. That means I don't power down my music server/NAS. It would take about 20 minutes to bring the server network back up if I turned it off (components have to be brought up in a particular sequence).