I agree with you generally, but that would not work on a SWAT op ("Before an op, one and ONLY one LEO should be designated as the person to give commands"). That might work in the first room, and even then, it would work if you happened to encounter only one person in that first room. After that, you don't know what team members are going to end up in what room, and which rooms will have individuals in them. "Police, Search Warrant!" should be getting announced the whole time, when not giving commands.
But I do agree that multiple people should not be shouting conflicting commands.