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

You SHOULD keep class D amp on 24/7.

A reliable surge protector might not help if lightning strikes, so if that's the case of such vulnerability, than turn on and worm up for 20min and than enjoy the tunes.

Class D amps as no other amps can be on stand-by forever. It will make their life longer than if they're completely turned off for months.

Transistors live longer when they're always ON.
They have life of up to 60k hours when ON and much shorter than OFF.
Electrolytic caps also benefit from being always ON except if under high temperatures. Leaving on even clas A/B amp isn't a problem if one does not dissipate excessive heat. The only now consideration is power line and if there's ever been an issue with lightning strikes. Than you will have to power down when leave home or at least when disaster is expected. There will be no surge protection of components if hit by lightning.
Class A solid state amps and tube amps always should be turned off when not attended.