Good point, Peter. It is less expensive to automate processes over people.
But I am actually not talking about replacing people with machines. I am talking about shifting limited human resources from the physical to the virtual. Right now, agencies have a hard time justifying the use of full-time employees for the express purpose of online engagement. The best that most government agencies can do is assign a portion of a person's time to online engagement, but that may not be meeting an agencies engagement needs with a group of citizens that prefer to access and interact with government on the Web.
To build on your private sector example, I'd like to see more agencies have a web-based chat feature similar to my direct access to customer service representatives at Bank of America or a CDC Cares on Twitter similar to @ComcastCares. Make sense?