I guess the question is, why do you need a client? I find most web interfaces to be sufficient
Clients like Thunderbird download the mails for a local copy. That means, you can a) read and search your mails offline, b) backup all mails. That’s not all. Such a client also: c) allows a unified interface to all different mail accounts from different providers in one view, d) better integration into your system, such as tray icons for notifications.
Everyone does their thing, so not saying you are doing it wrong, just giving you reasons to use an offline mail client; as you asked why.