Why do I get notified of bounced emails?

How the bounced email feature works is whoever sends the estimate or invoice will be the person that receives the bounce notice.  
By design is that the employee who sends the mail to the erroneous address will get the bounce notice and a "Hard Bounce" note will appear on your email activity page off of the dashboard.   It makes more sense that way since the person sending the estimate or invoice most likely has more understanding and interest in that email arriving to the customer than any other person in the organization.