Yes, limiting it to some minutes was just a first idea, to limit the amount of data on the RaspPI.
But thinking about it a bit more, I have to say, I came up with a bit more decoupled "architecture":
Octoprint sends out a MQTT message when print starts, including the address of the WebRTC string
A server/Docker container/whatever in my local network with a NAS share mounted, reacts to the message and starts to record the stream
Finishing the print, Octoprint sends a MQTT again to stop the recording.
I still have to figure out, whether WebRTC can do multicast/broadcast or is just peer to peer. Never done anything with it. But sounds like a fun little project