A lot of the strollers you do see in Tokyo fold up small as - or smaller than - ours does. We had no problems storing our stroller (Quinny Zapp) back on the Shinkansen from Sendai. Didn't even remember it as an issue.
What I do remember thinking when surrounded by the fashionable young couples in the taxi queue with small children strapped to them was how much wider the social demographic was for doing this than in the UK (and Spain).
I wish I could delve more into why this part of Japanese culture is different. I've seen glimpses of information disseminated publicly that supports carrying children (such as a documentary style segment on a Japanese TV program which explored the view that carrying small children for a large portion of the day makes them more intelligent) but as I don't read Japanese it is difficult for me to explore this subject with the thoroughness I would like to.