Unacceptable? How often does that happen (> 10 years?) without one having an old computer lcd from 2016 as backup in the cellar? Or a dirt cheap mini hdmi 7-inch replacement ordered overnight on Amazon?

Aside my guess is the Apple TV does usually work “headless” in OP use case with music playing controlled from his phone. One only needs a tv for streaming video (obviously) and I think for initial setup.