Why might the user's email address not show up in Views Send or as a Token?
YAY!

I finally managed to find out why this was happening by comparing against two other Drupal sites where Views Send behaved as expected. 

The issue was with the Views Contact Form module : https://www.drupal.org/project/issues/views_contact_form  

If you have that enabled, it breaks Views Send by hiding the main user email address, even if you have the format of the field set to plain text.