Non-editing teachers can't see student email addresses if they are marked as hidden in student's profile.
The role setting "View hidden user fields" does not allow this, although the implication is that it should.
To let n-e teachers see student emails, we've had to set "Enable/disable email address" in the role to "allow", which is more power than the n-e teacher should have. We don't want them to change it, just see it.

Suggested solution is to make "View hidden user fields" display hidden email addresses, the same as other "hidden" data.