Electronics degrade by cycling on/off , true but to what extent ? leaving on 24/7/365 equals 8,760 hours per year , since most power/filter capacitors are rated for 10,000 hours which would you think causes the most degrading ? How often do you plan on replacing the electrolytic caps ? how long do you plan keeping your amp ?
Newer amps have standby modes , older ones are on and off only . The new Krell 800 watt mono block uses 1 watt in standby and 260 watts on with no music so leaving it in standby is like turning it off , you wouldn't leave it on using 260 watts would you . My 250 watt amp uses 84 watts at idle/on , there isn't a standby mode so leaving it on is not very practical .
If leaving your amp sounds better to you then do so but think about the true cost depending on the amp you own .