It isn't, but keep in mind that this is still a pseudo feudal system, which still has existent Noble families with laws favoring them on the books. In a feudal system, that is absolutely how a 'police' (private army) force actually works. If you're the Prince, you can command them. In such a system, it wouldn't seem as strange that the daughter of the house is giving the commands. You'll notice they also all announce themselves by House first.

As an aside, if you are Amelia Bones, and you have to give one person preferential treatment, control, and ease of communication with your Aurors (and by extension, yourself), who do you pick from the group of kids who are making the announcement? Which one do you trust most?