Would like to control volume (TV's built-in speakers) with my iPhone via Apple TV Remote app, but no volume controls there.
Volume control through the phone app requires the use of a compatible AV receiver that supports volume control over HDMI-CEC. Not all equipment with HDMI-CEC option supports volume control through that. With such equipment, you would use the hardware volume controls on the side of the iPhone to adjust the volume.
Control your TV or receiver with your Siri Remote or Apple TV Remote - Apple Support
On a side note, I use the old Apple-branded 1.8m HDMI cable with my Apple TV 4K (and clearly get 4K picture). Why does Apple.com say that this cable does not support Apple TV 4K when it clearly does?
Did Apple at one time sell their own brand HDMI cables? I didn’t know that. I know they currently sell third party HDMI cables through their own Stores, though.
To answer your question (in short), it is about bandwidth. HDMI cables currently exist is four classes: certified for 5 Gbps, 10 Gbps, 18 Gbps, or 48 Gbps. The bandwidth use depends on several settings: resolution, frame rate, dynamic range, chroma subsampling. Use of the 10 Gbps or 18 Gbps cables can be sufficient for 4K, except for Dolby Vision, which requires the 18 Gbps cables. 48 Gbps cables provide no benefit, as the current HDMI port on the Apple TV 4K isn’t able to output that much data.
A long answer could go into much more detail and dependencies, if there is enough interest for that.
