Maybe I didn't make myself clear.
Assigning a ticket to a single Agent does not prevent other people from working on a ticket. Because the Ticket is also either in a Department or in a Team.
Transferring a ticket to another department does not change or clear if it is assigned to an Agent... nor should it. There is a valid use case where agent A (in department Foo) needs Department Bar to complete an issue. So they transfer it to another department and since it is still assigned to them they can follow along the status of the ticket.
There are a number of ways to clear or change who a ticket is assigned to, Transferring is not one of them.