The default groups don’t quite operate in a consistent manner as users/staff might expect. A lot of permissions and settings are tied to these default (I call them “special”) groups, and it would not always be appropriate to send email to them (not just admins or moderators, but also TL0-4, and everyone).
That being said, I use groups and incoming messages on several sites and none of my sites have so many users in a default group that I have issues managing them for group inbox purposes.
So there might be a Contribute > Feature request to add incoming email support, or one that addresses user management for new groups. 