it is worth noting that we have transportation systems where you get into a slow moving vehicle that then speeds up. the cable car is a lot safer than a faster moving sidewalk because you can just get inside and sit down securely.

of course, it takes up a lot more space and costs a lot more money.

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

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.