As with so many things there are two schools of thought and few will be persuaded to change sides. No surprises there of course.
There seems to be no definitive proof that moderate cycling (a few times a day) has any significant effect on modern devices in terms of failure before an end of life for other reasons. (Most hard information relates to continuous operation in data centres.) Years ago many people got fed up with the time taken to boot a Windows PC, so left them on all the time. To counter the "waste" criticism of this practice they used the reduced life argument, from the days of valves, and I think that now forms a large part of the leave-it-on argument.
OTOH leaving something like a FOX running 24/7 uses about £25 a year in electricity, with a corresponding environmental impact, so for me that tips the balance firmly to the side of letting them power down to standby when possible.