If you're still worried that robots will be too human-like, consider what happened to men's jobs when women, who not only are human-like but also are actual humans, increasingly entered the labor force. Men's jobs didn't decline; they increased. In 1950, before the large entry of women into the U.S. labor force, 43.8 million men and 18.4 million women were employed. By 2015, women's employment had skyrocketed to 78.0 million, while men's employment, far from shrinking, almost doubled to 84.4 million.
The simple fact is that the amount of work to be done in the economy is unlimited. What's limited is the number of humans, which is why the late population economist Julian Simons called humans, in a book by the same name, the "the ultimate resource." There's a story--perhaps apocryphal but no less insightful for that--about an American engineer visiting China in the 1960s, when the Chinese government was building a dam. The American, noting the large number of workers digging with shovels, told his Chinese host that the digging could be done more quickly if the Chinese used steam shovels. "Oh," answered the host, "but then there would be fewer jobs." "I didn't realize that was the goal," answered the American, "but if your goal is jobs, you might consider replacing the shovels with spoons."
What this story illustrates is that although jobs are important for creating value, if we can create the same amount of value with less input, it's wise to do so. Who, for example, wouldn't want an innovation that allowed them to do their current job and be paid just as much, while working half the time? This is not a fantasy. Pay is closely tied to productivity. The hypothetical innovation would destroy "half a job." And we would love it. We would use that freed-up time for leisure, or, more likely given our unlimited wants, for doing other work that gives us pecuniary rewards. That is the story of economic growth.