Sometimes it’s just more time effective to give the user some extra control. It can be very time consuming to assign the proper rights to shared mailboxes. There is always somebody who needs access en somebody who doesn’t need it any more. The service desk can get a lot of requests. These requests have have to be approved by somebody, and then the request has to be executed. It might be a lot simpler to assigning an owner to the mailbox which can handle the request themselves, and assign the proper rights.
Now in Active Directory you could assign managers to security group which could then edit the group membership. In Office 365 this is a little bit harder to do, but it is possible. In this blog post I will explain how this can be accomplished.