Controlling Apple TV volume with iPhone as remote

The volume buttons on iPhone, when the software remote is active, can work with select receivers and soundbars that have support for volume control over CEC (through the Apple TV box). I am not aware of any TV that has support for listening to volume commands through other HDMI devices.

None of the CEC commands have mandatory support (other than CEC passthrough to other devices in the HDMI chain). Manufacturers can pick and choose which functionality to bring to their devices. Some settings may not work with all devices.

I think these considerations may play a role:

Controlling volume at the input, gives a false sense of volume output settings, possibly causing shocks when changing sources (e.g. not as soft as you thought it was).

Additionally it may cause a bit of distortion as your ear’s frequency response is not linear. The perception of balance between low notes and high notes is different at different output volumes, but that can’t be managed or processed at the audio system when only the input volume changes.