In order to track student use of the messaging feature, students could have a dropdown box to select the class that the message pertains to. Only after selecting a class would the text pane show up to allow them to send a message. Maybe the student roster could appear for them to select recipients. Then a teacher can view the use of messaging to ensure it is appropriate and on task. If a student abuses the privilege, then the feature for that particular user can be turned off.
How can a teacher review the messages?
I agree, with the additional caveat that students should not have access to student inboxes - there should be the ability to permit specific role-based communications based on the classes a student is enrolled in.