The smart plug would turn it off and on, you would leave the amp on. If you're leaving the home for an extended amount of time mark the dial and turn it off. Like you said, there's always ways around if trying to save some cash. I own this little amp Fosi and it has tone control + a switch on the front if that any value to you. Currently only $56 bucks.If a trigger input exists, that would make things easier. But yeah, there are ways around it.
The Ayima or so is turned off by turning the volume dial... so unless the power socket is controlled, you can't turn it off or on without changing the volume.
If you only want to listen to music, I'd simply get a Wiim mini. Support for Tidal Connect is essential, and I don't think the ATV offers that?
I don't own an ATV so I can't comment on that.
My FlexHT just arrived today! Sure ill be sharing some of my experiece one here.