Technological change and automation absolutely can, and have, displaced particular workers in particular economic sectors. But technology and automation also create dynamics (for example, falling relative prices of goods and services produced with fewer workers) that help create jobs in other sectors. And even when automation’s job-generating and job-displacing forces don’t balance out, government policy can largely ensure that automation does not lead to rising overall unemployment.The catch here is that the displacement of workers by technology and the investment that re-absorbs workers displaced by technology are largely, but not entirely, independent factors. "Government policy" in the quoted paragraph is just another name for investment. Hans Neisser observed in his 1942 article on technological unemployment that "it is impossible to predict the outcome of the race between the two [investment and displacement] on purely theoretical grounds."
The conclusion is inevitable: there is no mechanism within the framework of rational economic analysis that, in any situation, would secure the full absorption of displaced workers and render "permanent" technological unemployment in any sense impossible.The "robot apocalypse" is neither impossible nor inevitable. It is probably unlikely, but unlikely things do happen, especially when people become complacent about the impossibility of unlikely things happening.