Can you leave class D amps on and not ever turn them off?

Do what maker recommends.   Bel canto recommends my amps be left on so I do normally except if away for more than a day.   Class D should draw minimal power when idling and does not generate much if any heat due to efficiency so that makes it more practical in general.

FWIW, the BEl Canto ref1000m amps draw a lot of current when powered up.    If I power both up at exactly the same time, my circuit breaker will break.   Once on though there is never an issue.

So a major power draw event like that is likely best kept to a minimum and is an indicator to me that its best to leave them on if possible.

Regarding sound quality when leaving on versus turning off,   I suspect leaving it on at it should be only helps but have not been dissapointed either to-date after firing it up cold.