Can't get HomePods audio output with Apple Music Sing and iPhone microphone input!

I have a pair of HomePod Minis that are connected to my Apple TV 4K Third Generation, as a stereo pair. When I try to use Apple Music Sing and my iPhone as a microphone with this setup, I get a message that I have to use only the TV speakers, and not the HomePods. Is this right? It seems to defeat the entire purpose of having Apple Music Sing, if I can't sing through my iPhone and get the output through my HomePods!