Some time ago, a user sent a request specifically for a new shared mailbox, that all users should be able to access. When we asked why they didn’t simply use one of the already existing addresses for the use, they said something to the effect that, while there should be no restrictions on accessing the mailbox, only those who wanted to receive email to it should do so. At this point, we started questioning why they had ordered a shared mailbox, rather than a mail group.
As I explained in an email to that effect, mail groups and mailboxes are quite different; a mail group simply forwards all email to the members of the group, while a mailbox must a) be actively accessed, and b) was limited in how we could control access to it, which (in Exchange 2013) is done with two permission settings:
Full access – this permission allows users full access to all features of the mailbox, though they are not allowed to send as the mailbox
Send as – this permission allows users to send as the mailbox
I suggested to the user that a mail group, would serve the purpose rather better than would a mailbox, and in the end, that is how we dealt with the request.