I'm sure someone has thought of these before, but I've never heard of them being implemented.
Email that was only relevant the day it was sent and has *zero* long-term value is nevertheless stored for years, backed up a zillion times, lovingly restored alongside today's mail after a loss, etc.
Allow and/or force users to choose a length of time that a message will remain relevant when it first comes into their inbox. For a meeting notice they can hit 'One Week'; for an order confirmation 'One Month'; for an HR form 'Three Years' or 'Forever'. Then they can forget about less effective methods of cleanup, because the mail will be discarded after its period of relevance has passed. They can do the same for sent messages, to keep their sent folder respectable. And, in an integrated client/MTA system like Zimbra, that setting could even be used as a preset for recipients in a custom header. So when someone (or their calendar) sends out an email about an event that is going to happen on Tuesday, the recipients see it marked 'Relevant for one week only' by default.
Each day, users are prompted to review their correspondence from 90 days ago and separate the keepers from the trash. This is low-flow, has the hidden advantage of reminding people about things they may have forgotten, and seems like it could make a huge difference in the amount of irrelevant email being stored, either alone or in combination with the first solution.