there are many that will do this one way or another, 12volt triggers or eArc over HDMI,it mostly found in surround receivers or speakers such as Sonos
as there in a constant state of somewhat on.
so pioneer Yamaha and the other usual suspects. 2 channel amps i personally don't know of any
Another way to do this in a similar way is to use a Logitech Universal Remote that let's you define 'activities' as Logitech calls them. You do need an amp with a remote control for this to work.
Example. We have an activity called TV. When I choose that, the TV powers up, switches to Digital, our network stereo receiver powers up, switches to optical input 1 (connected to the TV). If I want to listen to our record player I choose the activity Phono. The TV powers down and the receiver switches to Phono.
Shutting down is also very easy. You simply switch of the activity on your remote and everything that was on in the activity powers down.
Our Yamaha R-N602 network stereo receiver automatically powers up and down when I use Airplay for streaming. That works separately from the Logitech remote.