There also used to be "central turbines" whereby there was a central spinning rod that one could attach belts to in order to spin a thing to get work out of it...
There's a cool working example of this at Kelham Island Museum in Sheffield, England.
That was normal in the age of steam. Having lots of tiny steam engines on the factory floor does not make sense. Keeping them running is too labor intensive, they would be fire risks, and they’re less efficient.
And in the age of water, running shafts to the waterwheel was vastly easier than having a wheel at each station.
Really cool, sort of like how an ICE drives ancillaries
Cool indeed, but pretty dangerous and difficult to reconfigure. Electric wires and motors are so much smaller, and easier to protect, and more interoperable, so you can see why they won out.
That was one of the reasons behind having factory whistles: all workers take their places, the whistle, then the whole thing is started. While it's running people are not supposed to move around.