They are not. This is something a host must do from within their hosting management system and Cron. to pipe certain emails to support tickets.
It is better to have a specific email address that will do this, but then even so the ticket generated would not identify the client, so still unknown if it is the client communicating with you.
On top of it, its difficult to assign a chat regardless to whom ever needs to take care of the situation. Ticket allows you to send the exact details to whomever needs them. When I get phone calls from my local clients. I make a ticket for them. So we know the date it occurred what the issue was etc.
You get into to many communication issues otherwise. (example) Lets say I find out a week down the road a repeated issue that seemed to be user related is not. With tickets I can look quickly find similar examples of the same issue and then send it to the appropriate technician.