More likely, that's correlated with something else that is the real explanatory variable (history, etc...). John Kay had a good article on a similar topic: http://www.johnkay.com/2013/01/16/london%E2%80%99s-rise-from...
So no, you don't need a flat grid to have great public transit.
Best to compare San Francisco with...Lausanne...or Chongqing (or any city with a bunch of hills that is fairly vertical).
How fast can you get from 4th & King to the SJC?
Nevertheless, comparing San Francisco to Lausanne is unfair. Lausanne provides better infrastructure for a smaller population.
Tokyo is in no way even close to flat. It has some flat areas (e.g. landfill in Tokyo bay), but there are huge numbers of very hilly areas as well (including many popular commercial hubs and densely populated areas in the city center). Not gentle hills in many cases either, but quite steep.
[... and if you go to the outskirts, there are actual mountains within the Tokyo city limits!]
One difference with with SF, of course, is that Tokyo roads don't form a rigid grid that ignores the topography....
> Japan cities spend a lot more money on infrastructure than even American cities
Tokyo mass transit is overwhelmingly private (owned, run, and financed), especially if you're talking about rail.
The Angel's Flight Train is still there.
The worlds oldest Freeway, the 110 goes through a valley.
The 5, 101, 10 and 60 wrap around all kinds of hills within a few miles of downtown LA.
Limited horizons and change make things interesting. You don't want complete chaos, because things also have to "make sense" to some degree (so complete randomness, like a stereotypical suburban cul-de-sac maze, tends to be bad), but variation is a good thing.
[A nice city to look at for interesting approaches to urban structure which are both somewhat regular, but more interesting that a grid, is Edinburgh, which has seen successive waves of fairly successful urban renewal over centuries, resulting in one of the most beautiful and fascinating cities in Europe. In the "new" parts (150-250 years old as opposed to the older and more organic medieval parts), Edinburgh streets have such features as small localized grids, sized as to with care to avoid large-scale monotony, occasional "circuses" acting as focal points, streets in gentle arcs which are practical for transportation, and yet maintain a constantly evolving street view and horizon, terraces along the sides of parks, etc.]
It's a localized example of the effect urban structure can have, not a denigration of the entire city. So, please, don't take it as a dig against Chicago; I rather like Chicago in many ways, and much of my family lives there. I used the above example only because it's one of the more extreme cases I've encountered.
As for the "it's easy to find addresses!" argument in favor of large-scale grids, well, yes, but in my experience this is fairly unimportant for the actual residents of a city. Most people don't spend any significant amount of time travelling to completely random locations, and to the extent they do, every city evolves methods of way-finding that suit it. I think it's much more important for the residents that the city actually be a nice place to live, and part of that is being beautiful / interesting.
[For tourists, yeah, extremely simple way-finding can be a significant advantage, but I don't think cities should be designed for tourists over the needs of those who live there...]
Salt Lake City grid system was also not designed for tourists. It was designed for travelers, yes, and I believe it was part of the vision that SLC would be looked at as a model city, with a strong Cartesian/classical influence. According to Wikipedia, "In these western cities the streets were numbered even more carefully than in the east to suggest future prosperity and metropolitan status."
Also, a grid system made it easier to subdivide the land which was newly part of the US.
So to say that the grid system is influenced by tourists is a bit of an exaggeration.
[I lived there in the '90s, though, and I'm a bit scared to return for fear that the city has been ruined by its new-found position as a seat of "power" (haha); the sharp-suits crowd, "gotta pave over that park and widen those roads for my flash car!", etc...]