I think there's a secondary aspect here as well. I walk a lot and always have. And while I almost never feel I need to walk 'fast', I've observed that my comfortable walking pace is a lot faster than most people I know who don't walk every day, even when I'm in no particular hurry.
I can confirm it and have to add that it's the same with riding my bike. Moving at a "normal" speed becomes even somewhat hard when with other people who always tell you to slow down (because when you are not paying attention, you are already speeding up again).
(Mass transit because you’re more likely to see commuters! Outside big cities you will measure fewer people walking to work, because they drove).
So, strongly correlated with economic activity and cultural factors around timeliness, but no deep psychological explanation required.
I walk fast in the city when I’m going to/from work or trying to get somewhere on my break.
I don’t walk as fast on the weekends, and tourists in the city certainly seem to be in no particular hurry (at least, it seems that way when stuck behind them clogging up the footpath).