Thanks for everyone's ideas. I wish I had more to contribute to the discussion myself, but as mentioned in the original post, I'm only at training for my private and my knowledge of the industry is nowhere near enough to guess at how/if/when companies would try to bring in fully-automated computer flight systems.
Seems to me that I won't have to worry too much about being made obsolete. Security concerns, the limitless possibilities of things that can go wrong and possibly not accounted for in code, lifespan of aircrafts, and public unwillingness to fly an unmanned aircraft probably make the job of a human pilot fairly secure for a fair while anyway. I do wonder about the nature of the job that I would face in ten or twenty years time still.