Part of their job is to write reasonable responses to customer inquiries. That's the output of their working time, for which they are paid.
Saying that should be private is like saying someone's code check-ins should be private.
And if we assume people are good rather than bad, it's a chance to show off, without ego, a particularly good response and/or responder. That gives them a morale boost from knowing their boss and co-workers saw them doing a good job in a natural environment, and it motivates co-workers to do a similarly admirable side.
Saying that should be private is like saying someone's code check-ins should be private.
And if we assume people are good rather than bad, it's a chance to show off, without ego, a particularly good response and/or responder. That gives them a morale boost from knowing their boss and co-workers saw them doing a good job in a natural environment, and it motivates co-workers to do a similarly admirable side.