@alehandrof’s suggestion matches how I expected the messages system to work.
I’ve had to use groups more for emailed-in support messages, and it feels extra messy and a little confusing for such messages to be separated from my inbox and even my moderator group inbox (due to not being able to set an email-in address for the mod/staff groups). I can understand that for many this system of dividing by group is useful, but for us it splits things up with no benefit that I can see.
to the feature suggestion of a unified inbox profile setting, or to a plugin that would do the same.