The private sector has already started doing this. Airlines charge higher fees if you book on the phone or in person rather than online. Banks have added fees for live teller service. Almost all customer service functions for the private sector have migrated either on line or to recorded telephone support.
Governments at all levels face severe spending limitations over the next several decades and machines are less expensive than people. Yes the level of service declines, which shows up in customer satisfaction surveys, but so does the cost. Given a choice between paying the taxes to support a fully staffed DMV vs renewing licenses and registrations online, most voters choose the online option.