It's far more than a nice idea that will not work. Just work in a place where hundreds of scripts send out thousands of emails a day -- I've had more than one job with those parameters -- and the alternative is not only desirable but eventually necessary. Doing systems administration via email trail is a way to waste alerts, fill email boxes and waste admin time.
No on-the-job script should ever send out an email alert. It should alert a monitoring tool, such as the aforementioned Nagios. A higher end layer of software, or a help desk, can decide to alert admins *if necessary*. This is the kind of thing that a smart shop can automate and a foolish shop will drown admins in electronic paper.
Things get missed in floods of spam. So the smart thing to do is stop the spamming, consolidate the reporting, and push the alerting to a decision making layer. Status messages can then be consolidated in a web interface, as they should be.