SOUTHCOM's Small Wars Operations Research Directorate (SWORD) we used to call ideas like yours the "almost obvious" - that is they should have been obvious to anyone with half a brain but were not until somebody actually stated them!

As an old Reserve guy, that is one I should have seen, but didn't. A USAR MP unit with the mission to train foreign police in both a constabulary and community policing role makes good sense and could be tailored to include a significant interagency component like ICITAP and various state and local police organizations.

then we get to the practical: Where would it be based? How would it drill? who would be recrutied to staff it?

sounds like fun!