They actually do send emails like this, believe it or not. Here's the text of one I received in January when my bag wasn't loaded onto a connecting flight on time. Perhaps they are only triggered when DL is 100% sure your bag didn't make it (e.g. scanned in departure city after your flight is airborne or something), but I had this in my inbox by the time my flight landed at my destination:
Dear FIRSTMIDDLE LAST,
We are contacting you because your bag(s) did not travel as intended to your final destination.
We are doing our best to get it to you as quickly as possible. Please proceed to a Baggage Kiosk
located near the Delta Baggage Service Office, or see a representative at the Delta Baggage Service
Office for additional information and assistance with completing a mishandled baggage report.
We apologize for the inconvenience. You can get the latest tracking information for your bag at
delta.com.
Thank you for choosing Delta.