From my personal experience, it is much better to leave them on 24/7. Letting them sit or turning them on and off causes failures.
Sitting in less than ideal conditions causes corrosion. Keeping a system always warm and running in such an environment can help stop corrosion problems like in chip sockets.
But at the same time this dries out the caps faster. Caps help regulate voltages. Also switching circuits give a "kick" at startup. Once the kick is in, it's not needed until next startup. So.... long running trusty equipment finally has a loss of power for any number of reasons. You try to power it back on, a switching circuit tries to kick, but shorts out instead because of a dry cap. It now fries many more components long with it. Once again giving rise to the legend of "leave it running". If instead the system had it's worn out components replace ahead of the failure.... it would run for a long long long time despite repeated power cycles.
My experience.... 32 years in equipment repair.
Plaz