In my opinion it basically is a must have, to always receive push-notifications about new emails and reminders from your calendar, not only when the window is open (minimized is basically the same as open).
That is, why I think it is an important feature to have a persistant icon in the system tray, in which Thunderbird launches on boot (start minimized to tray) and when clicked on, it opens the window.
When closing the window, instead of exiting, it should go back to being minimized in system tray.
There were add-ons which did this exact same thing (FireTray and MinimizeToTray with their many revivals), but with the deprecation of the old add-on API this has now become impossible.
There are some projects trying to fix this problem, like BirdTray, which have their own separate program running the entire time, which of course consumes way more resources than if Thunderbird could do it natively. Furthermore, the ability to minimize to the tray instead of exiting cannot be replicated that easily.