I suspect their objections come from traffic analysis (adversary sees that phone A sends messages to a lot of others→must be a commander or so; a burst of traff

I suspect their objections come from traffic analysis (adversary sees that phone A sends messages to a lot of others→must be a commander or so; a burst of traffic among phones marked as commanders in an unexpected moment→something is being planned, etc.). Also, availability if Internet of cell coverage is cut by the adversary.