I don't have much knowledge regarding mail but I can think of two reasons.

First is the use of mailboxes if your mail provider does not provide you with an IMAP server to connect to in which case you'll use a client like mutt to manage your mails.

Second one is the accesibility through the terminal could be reduced with HTML sites. If I want to access my email through a headless server using lynx or similar having to refresh the website to check new mails, or even composing them might be difficult.