For the businesspeople in my office, the answer is to just leave them in your mailbox until the retention policy gets them, or print them to PDF. I don't think anyone works with .eml directly.
In the early days of my IT career I had an executive who had his secretary print all of his emails on paper and put them in an IN box on his desk... Never had an IT complaint from him either. FYI, this was in the mid 2000s, how the meteor missed him, I have no idea.