I think I have figured out what is working and what is not. The one combination that works is ATV4K + HomePod + same room. And that’s it. If you don’t have that combination, the “Default Audio Output” option does not appear anywhere. In the Home app, if you change the room of a HomePod to a room that has an ATV4K in it, it asks you if you want to set it as the default output. If you later try to move the HomePod back to its original room, it asks you if you want to move the entire stereo system to that room, or just the HomePod. This does not work for non-4K Apple TV’s, and it does not work for the HomePod mini. Nor does it work for any other AirPlay outputs. This is deeply disappointing to me, as I have speakers in the ceiling of my kitchen connected to a cheap amp connected to an old Airport Express that plays the audio from the modest TV on the wall just beautifully. I have a HomePod in a room that needs a HomePod. And I have the 4K Apple TV in the room that needs that. But the kitchen needs neither. This is a puzzling omission, because the only thing required here is that a default output be remembered, instead of users having to set the audio output by hand every single time. I think there’s enough room in the memory of my non-4K Apple TV to remember that. I am not one who is prone to suggest that Apple creates these kind of restrictions to force us to buy new products. But I am having difficulty seeing the technical reason why my Apple TV 4 cannot reliably remember to output its audio to a certain set of AirPlay 2 speakers in the same room.