I know a librarian who spends an inordinate amount of time helping the elderly and tech illiterate members of the public with creating emails, because they're necessary. However, you can't create emails anywhere without a phone number these days - a post office option would fix that.
Email already gets enormous amounts of spam, and the only reason most don't see it is because private service providers like Google expend resources filtering them out. Why would a business not be able to charge for premium filter services on an email they don't host? Not to mention that private email services send you ads.
To be clear, I'm not saying we should shut down Gmail tomorrow, but having a free public email service option would allow many people to use internet infrastructure they don't have. It's an accessibility problem that should be addressed in the public's interest as well as shareholders.