Robin Hanson agrees with me that machines will eventually completely displace human labor, though he doesn't have as many nifty charts as I do.
Right now, computers and other forms of machine intelligence aren’t nearly sophisticated enough to emulate the human brain or replace human labor on a global scale. But in the long term — say, a century or two in the future, as artificial intelligence becomes far more sophisticated than it is today — the picture could be far different. For now, it would be insufficient to merely have more powerful machines, if they continued to mainly complement human labor, as machines have for centuries. When machines complement humans, better machines lead to more, not less, demand for humans.
Even if machines have so far tended to complement humans, might machines someday become actual substitutes for human workers? The key thing to understand here is that while a machine might substitute for a human on any particular task, when the division of tasks between humans and machines is stable, then cheaper and better machines raise the demand for humans.
But if machines could effectively replace humans for most tasks now performed by humans, that would be a very different story. Full-time human wages would then become small compared to humans’ income from owning machines that do the work. This isn’t the current trend, so don’t worry about it happening soon. But not only is this possible, it is likely, within a century or two, through the use of “whole brain emulations.”
I think that "within a century or two" is far too long of a time line -- I wouldn't be surprised to see it happen within my lifetime. (Of course, I'll probably live a few centuries, so....)