There are times when a message is sent to the shared inbox for informational purposes (i.e. policy change notifications or customer account changes.) It would be great to force each member of the mailbox to review the email and then close it once reviewed by all parties. This could probably be accomplished with a "To Do" if there was an option to assign the To Do to every user of the mailbox. An option like "assign to all mailbox users" or "force review by all mailbox users".
Currently we have an approval option when a member writes an email that it first needs to be reviewed by one or multiple members. However, we do not have a similar workflow for incoming messages.
That said, and as you suggested, we could accomplish that with the To-Do's. The only thing that prevents this at the moment is that a To-Do can only be assigned to one person.
If by enabling the assignment to multiple members is an acceptable solution for you, we can make an endeavor to change it. Let me know.