Why did it take human beings so long to reinvent the wheel? As Scientific American explains, it didn't. What took a long time was inventing the axle.
The tricky thing about the wheel is not conceiving of a cylinder rolling on its edge. It's figuring out how to connect a stable, stationary platform to that cylinder.
"The stroke of brilliance was the wheel-and-axle concept," said David Anthony, a professor of anthropology at Hartwick College and author of "The Horse, the Wheel, and Language" (Princeton, 2007). "But then making it was also difficult."
To make a fixed axle with revolving wheels, Anthony explained, the ends of the axle had to be nearly perfectly smooth and round, as did the holes in the center of the wheels; otherwise, there would be too much friction for the wheels to turn. Furthermore, the axles had to fit snugly inside the wheels' holes, but not too snugly — they had to be free to rotate. [What Makes Wheels Appear to Spin Backward?]
The success of the whole structure was extremely sensitive to the size of the axle. While a narrow one would reduce the amount of friction, it would also be too weak to support a load. Meanwhile, a thick axle would hugely increase the amount of friction. "They solved this problem by making the earliest wagons quite narrow, so they could have short axles, which made it possible to have an axle that wasn't very thick," Anthony told Life's Little Mysteries.
The sensitivity of the wheel-and-axle system to all these factors meant that it could not have been developed in phases, he said. It was an all-or-nothing structure.
(h/t Brad DeLong)