It depends on the type of service. In some cases, all that matters is that the job is done properly.
Personally, I would prefer to receive quick and efficient responses from tax officials, even if the responses must be generated by a machine. I'm using this example because we're in the middle of tax season.
However, if I have questions about my health, if the discussion takes a more personal turn or if I'm ill and in hospital, I want to have a human in front of me. It doesn't bother me that the human uses technology to do a better job. That said, some situations involve human and relational concerns that are better addressed through human interaction.