That's been tried. Never Stop Railway, 1924.[1] The drive system is a variable pitch screw between the rails. Large screw pitch between stations for fast travel, much tighter pitch in stations for very slow movement along the platform.

Never tried again with that kind of drive, although there are park rides where the loading platform moves. This requires safety devices and staff to prevent people jams at the end of the platform.

[1] https://www.youtube.com/watch?v=EX_MlWL7YKM

I'm talking about aerial cable cars, which are plenty in use around the world today. https://www.youtube.com/shorts/X5qjnryYWQY

They are pretty common tourist transports in mountainous areas and ski resorts. They're even being used for regular public transport now. https://www.youtube.com/watch?v=vdTE4TCqkZo

And you can only hop on/hop off a cable car at predetermined locations. To keep average speed high, those tend to be spaced relatively far apart.

I’m not sure about the “takes a lot more space”, and I definitely doubt about the “costs a lot more money”. Using outdoor escalators as proxies, I suspect outdoor moving sidewalks will need lots and lots of maintenance. If you want to have some guarantee of service you’ll also need multiple sidewalks side-by-side.

To be fair, on all moving walkways today you can only really get off at the beginning and the end.