Automating data entry work or similar is one thing, there are many companies out there automating a high-value-added work like IT project management. Most of the work project managers do today will be automated in the coming years. Mark my words!
One thing that PM's do that I don't ever see a computer doing is managing clients/workers. It's the classic idiom: technology is easy, it's people that's the hard problem.
You're right about people being the problem but, as you said, technology is easy and in my work, I see how automation manages clients and workers.