Problem is finding stuff in your inbox. This helps with the noise problem from emails that will never be relevant again.
I think that working on the "email noise problem" when you could be building a profitable business helping people prevent or cure life-threatening conditions is a terrible use of brainpower.
This idea would only be good for spam "buy now before its too late" type emails (ie non-important information) which is not a problem that really needs solving.
As for generic expiry of individual emails, Lotus Notes has been doing that for years and years. It doesn't provide expiry of emails that go outside of Notes, but that is not what it's trying to solve. Internal data retention policies become much easier to handle if it's enforced by every user's mail client.