Modesty is an interesting point, I've heard an anecdote from a local touch-rugby team that they has been scheduled to play an exhibition game against a high-grade womens team, and were initially hesitant and overly-cautious when attempting to tag their opposition until they realized they were very good players and that tagging is tagging; there's no sexual intent merely because a hand contacts a breast, for example. The context made it acceptable sporting contact. Depending on cultures, that may not be an acceptable view, especially ones that value modesty.
That also reminds me of a smaller (IMO trivial but still interesting) point, of differing rules between sexes. In association football, I know some leagues allow women to cross their arms over their chest to soften the impact of using the chest to play an airborne ball down to the feet, provided they don't abuse their arms to propel the ball further. This would usually be seen as a hand-ball offense in the men's leagues, due to the intentional positioning of arms into a place likely to contact the ball.
It's tough to approach this materially when most of us are from nations with cities designed around car transport; not just the road layout but where buildings are located and such, which makes cars seem like a good solution to a world designed around them. Add on top of that the social aspects other users mentioned, such as 'freedoms' culture in USA, and the impressions given by their current public transport making it unpopular or even seen as a 'poor person' thing, I consider cars a status icon in most countries.
As a case study, Beijing has some restrictions on road space, such as [wiki] "restriction of cars that could enter common road space based upon the last digits of the license number on certain established days during certain periods in Beijing. The main objective of this restraint policy in Beijing is to reduce the amount of exhaust gas generated by motor vehicles.", which were apparently successful, even if temporarily.
This kind of system, even though it's not really what you described, is also being done similarly in other countries wiki: Road space rationing which lists:
Along with other cities doing temporary schemes, mostly in Europe.
I know it's a bit of a non-answer, and doesn't approach the redesigning/sectoring you discuss, but food for thought on society and not driving cars in urban areas.