@highend64, like most things in audio, it depends.
Obviously class A amps will run hot so best not to leave on but Class AB can and IMO should be left on all the time.
You'll probably remember the old incandescent light bulb that mostly failed on switch on because the filament is cold and at its lowest resistance and pulls most current = blown. This is stressful for amps at switch on.
When a hot amp cools down there is condensation so the PCB is contracting in the presence of moisture providing the ingredients for failed solder joints and corrosion on anything with some ferrous content. Class AB in its quiescent state draws very little power and does not get hot so just leave it on.
Of course if it is to be out of use for a long period then best to turn off.
Valve amps can also be left on if HV to the power tubes is interrupted by relay and the heater voltage to driver is reduced to 2/3 of nominal. So 6.3V can be reduced to about 4.2V via a standby switch thereby avoiding cathode poisoning. Flipping from standby to on will very quickly bring the heaters up to nominal V while the HV is delayed for 20 to 30 seconds before connecting.
Some but not many commercial tube amps provide this feature. Easily done using an LM 317 adjustable voltage regulator for less than $2