🏭 Why no Industrial Revolution in ancient Rome, Greece, or China?

Unfortunately, there's nothing new about the Down Wing enemies of progress

I don’t think about ancient Rome every day, but I’ll concede that the sword-and-sandals superpower does invade my thoughts from time to time. And this is the Up Wing question I frequently ponder: Why wasn’t there an Industrial Revolution in Rome two thousand years ago rather than Britain two hundred years ago? Or in Greece? Or China?

Consider: If there had been, humanity might have already achieved the status of a Type 2 civilization on the Kardashev scale, capable of harnessing the entire energy output of our sun. Such a civilization, as Carl Sagan speculated, “would bear little resemblance to anything we know.” At the very least, we’d have self-driving chariots, right? Instead, we're only barely approaching Type 1 status, barely able to utilize all the energy available on Earth. (And some folks would like to reverse even that level of progress.) 

So what went wrong? What didn’t go right? What was the missing ingredient?