HomePods won't play if WiFi is not connected to internet

I finally had my 5 HomePods working as two stereo pairs (bedroom and livingroom) and a singleton in the den.

Today I was listening as usual and suddenly the devices disappeared from iPlay and I couldn't play any music anymore.

My phone was still connected to WiFi. I found the problem and it shows how ridiculously flaky this whole scheme is. It turned out that though all my devices (phones, PCs, etc.) could connect to my WiFi, the router itself was not connected to the internet. I proved this to myself using a unix PC which allowed rapid enable/disable of both WiFi and Ethernet interfaces. When only WiFI was enabled, I could not ping outside of my LAN (i.e. ping 8.8.8.8). When Ethernet was enabled, I could ping outside my LAN.

My complaint is, WHY does HomePod require a connection to the internet in order to play music over my WiFi LAN. As long as the devices see each other and my phone, no internet access should be needed. OK, maybe Siri needs it, but I am not using Siri.

I suspect it is so Apple can collect information about me whenever I am using the HomePods. That is pretty lowdown.