I have been working with emails as a tool for the last 20 years. In different communities, setup, etc. I never felt overwhelmed by the number of emails, I have filtering strategies, I could talk about that in a separate post.
When projects using emails are going awry to havoc, most of the time is because people do not use emails in an optimum way. My main recommendation would be:
Always copy to an archived mailing-list. Never ever send private emails. (1)
(1): In the context of working on a project. Privates emails for HR, personal stuff, etc is fine. Anything which is about the project should be on a linkable, archived mailing-list.