Good filing systems generally make things easier to manage.
Being able to retrieve emails quickly and easily, and attachments, not only can save a lot of time and bother, but it can greatly help in difficult discussions with clients (or suppliers).
Reduce time where it is necessary to retrieve old emails and attachments.
Increase effectiveness, where knowing the audit trail of communications is important.
Knowing the full story (including communications by other staff) can help in any disagreements of misunderstandings.
Efficient and complete email filing may be part of an ISO certification.
Saving emails in more than one software platform (i.e. other than Outlook) adds to back-up safety.