At our university, the SIS_ID displayed in the People list and the Secondary ID displayed in the Gradebook are number-strings that are useful for big databases to match identities. We also have a username that is much more human-friendly and that also forms the first part of our institutional email addresses. That username is not displayed in any list or tool in such a way that an instructor can use it to ensure that the person whose record she is looking at is, indeed, the person she thinks it is.
A solution for us -- and we think others might find it useful -- is to allow the default email address to display to all instructional staff in the Grades list and alongside the student's name in Speedgrader. This would also be useful in Quiz Moderation and other places where student names are listed.
Ideally, the gear-menu in the Grades list could include an option to allow the instructor to hide the Secondary ID and the Default Email if desired, just as the instructor may opt to hide or show student names or the notes column. Whether this feature should be available to instructors should be a default controlled by the institutional admins. An advantage to this placement is that the Gradebook can already be exported, thus providing an easy way for instructors to extract a list of email address for their students, which can be useful in any number of ways.