Watch someone work a shared inbox for an hour and the pattern is obvious. Opening and reading each message takes seconds. Everything after that is the real cost.
Each email forces a chain of small decisions: who owns this, is it urgent, has someone already replied, what do we say. None of those decisions is hard. All of them interrupt whatever the person was actually hired to do. Add up your own numbers: messages per day, times a few minutes of deciding and forwarding each, times whoever's salary is doing it.