You've gotta be referring to escalators here. Never seen a moving walkway in a big-box store, or a subway station for that matter.
https://en.wikipedia.org/wiki/Moving_walkway#Trottoir_roulan...
Speaking of speed, in the Stockholm main station the escalators go faster than others I've experienced... But I don't know if they've adjusted the speed since my experience years ago.
I do think a concept with parallel tracks moving at different speeds would have been easier to use and more reliable though. But it might not have been revolutionary/over-engineered enough to attract attention and subsidies.
I have seen some occasionally in stores, in or around Paris. They usually are on an incline to allow trolleys to be taken up or down a level. Or similarly outside malls to get trolleys to the upper level of a car park. That’s in places where you have to stack car parks instead of just having them sprawl all over the place, of course.
> or a subway station for that matter.
There are a few of them in Paris métro stations. Some of them in the London Underground, as well.
Quoting wikipedia:
> The walkway has been the longest continuous moving walkway in the world since its construction in 1961.
I have never seen a flat one in anything else but airports or connections between other mass transit transports such as metros and trains. Definitely not in big box stores as they would be inconvenient and slower than pushing the trolley in the flat.