I expect any mail system inhabited by more than a few users who lack either common sense, an ability to read or an understanding of exponential growth has suffered this problem at some point.
When I was a PSO, the entire Brizzle Uni mail system ground to a halt after someone worked out how to CC all the course mailing lists into a message advertising their event, and people kept reply-alling to the reply-allers telling them not to reply-all. Those of us whose email was stored on the better-resourced engineering faculty server got to watch the fall-out in slow motion...