Two thought experiments: 1) Do you think the general public would support the use of self-driving cars on public streets as they operate today, even after seeing the DARPA results? 2) Do you think the general public would support the use of computers to diagnose cancer without involving human doctors anytime within the next 50 years?
Remember that when [specialized worker X] says their job can't be done by [new technology Y], they aren't just referring to the technology being unable to fulfill the task. There is a whole economic, political and sociological matrix on top of the job market that prevents technology from displacing workers, and certain regulated industries are more sheltered than others. The hospital is probably one of the most insulated working environments for technological advances (just take a poke at any of their EMR systems to see what I mean.)