New York City was supposed to have a variable speed moving sidewalk between Grand Central and Times Square
Dana Schulz at 6 Square Feet, a New York City real estate site, shows a 1951 proposal to replace the crazy shuttle subway that runs between Grand Central Station and Times Square. I have travelled on this once and thought it was completely nuts, that it should be a moving sidewalk. But although moving sidewalks were invented in 1871 and first seen in public at the 1893 Chicago World's Fair, and were a hit in Paris in 1900 (here is Thomas Edison's video of the Paris sidewalk in action....
...there is a fundamental problem; It is extremely difficult to change speeds, and humans can only handle so much of a change in speed. (I know this because when I was a boy scientist at 17 I made a patent application for a very silly variable speed moving sidewalk). It is a fundamental principle that goes back to Bernoulli and molecules: If you take the same number of people or things and make them go faster, they have to move further apart.
© Popular Science via Google Books
The New York scheme from Goodyear and the Stephens-Adamson Mfg. Co. deals with this by having customers get on a short belt-style moving sidewalk which runs at 1.5 MPH, then they step from that into a conveyor car which is running at the same speed. Once they are safely in that, it can change speeds which they claim can go up to 15 MPH. As you can see in the drawing, the cars are bunched together at slow speeds, further apart when they are fast. That's the fundamental problem that had to be solved. There is more detail here in the patent application. Alas, it was never built; the Budget Director, a certain Abe Beame who later became a particularly ineffective mayor of New York from 1974 to 1977, killed it.
There have been many attempts at developing variable speed moving sidewalks; even Randall at XKCD had some fun with it. The question is what you do with all the stuff when it slows down. Sorry, that is only one of the many questions, like how people hold on, where they stand, and more. Perhaps the best attempt at it was made by ThyssenKrupp with their installation at Toronto's Pearson International Airport. Watch my video and you can see how the pieces crunch together as one part dives under the other as it slows.
This works, but is incredibly noisy and is constantly being serviced, often out of order and closed. They have redesigned it so that every individual segment is running on its own linear induction motor and is less likely to break down, much like how they are powering their fabulous new elevators. It's a shame it didn't happen in New York 60 years ago. But then Delerious Pneu York didn't happen either.