Is there any danger in leaving a class D amp on unattended for ten days?

I agree that the fire risk is real enough to be concerned, and so is the damage to the environment. I have invested enough in energy saving and solar panels not to blow that with wasting energy on audio gear, even if it is relatively efficient Class D stuff as in your case.
I don’t believe my electronics sound better if I leave them on. That would be bad design.

How can you be sure an amplifier really does sound better when left on? Human sonic memory is not more than a few seconds, so you can only know if you compare two identical amplifiers, one left on for a while, and the other started from cold. To be honest, if there really is a difference (which in most cases I doubt), it would be a bad design.
Apart from the two disadvantages I already mentioned (fire risk and harm to the environment) there is of course another one: heat is the enemy of electronics. Leave your gear on and you will significantly reduce the life span of critical components.

Apart from the scientific articles that the ordinary Audiogon user does not have access to, here is the wikipedia article on auditory/echoic memory: https://en.wikipedia.org/wiki/Echoic_memory