why does this Dart broadcast stream not accept multiple listen calls
The getter onBark invokes asBroadcastStream a second time on the _barkController.stream. The newly created broadcast-stream will try to bind to the _barkController.stream but will fail because there is already a listener.
So yes: broadcast streams may have multiple listeners, but the asBroadcastStream method must not be invoked multiple times on a single-subscription stream.
One solution is to cache the result of your first asBroadcastStream.