Only alternative ?
Should it not be possible to configure the mailserver to count the number of outgoing emails and block with an alert when a limit is reached ?
If your org generally sends a few emails a day, you would set the limit at, say, 50. If you get a message that said limit has been reached, you have time to check the how and why and correct things before resetting the message count (larger organizations could also evaluate their mail sending habits, but I suspect they'll have more powerful tools at their disposition).
That should be rather simple to implement, no ?