This sounds more like a newsletter. Maybe a newsletter block would be useful, so site members would receive information relating to things that are site and not only course specific. However, if it is to be used this way, site members should be informed somehow, so they realized being registered on a site also means receiving e-mail from the site from time to time.
Currently old accounts eventually get unenrolled from everything automatically, so that email naturally dies out and people don't get spammed.
Maybe if users could completely delete their own accounts, but, would they ...?
Why would it be important to mail people who weren't in any of the courses? Maybe you just need an open course for the leftover people?
Hmm, this would cause problems for me I think. I have accumulated quite a number of site members who are not members of a course, and because they are not active on the site I don't want to send email to them.
However, a forced site level forum is perfect for sending messages to all my actual students if the message is the same for each class; this means I don't have to write it and then copy and paste the same message several times, but just write it once.
The current way of doing things works well for me, but if we had selection options as to which user groups could receive the email then perhaps we could please everybody...