There are a lot of comments here about why public transit in the DC area doesn't work, but nobody that I've seen has put their finger on it. The biggest issue is that the area covers two states, at least ten counties depending on what you count as the “DC area”, plus the District of Columbia, which isn't a state, doesn't have control over its own budget, and has no representation in Congress. Oh, and in Virginia citi…
Train companies own land/real-estate around each station. They open grocery stores, shopping centers, office buildings, hotels at many of their own stations. This seems to lead to a virtuous cycle. It's in their best interest to get people to use their trains.
Further, there's at least some competition as there are often 2-4 paths to get from one place to another. For example, you can go from Shibuya to Yokohama either by JR East or by Tokyu (different companies). You can go from Tokyo to Yokohama either via JR East or by Keikyu (again, different companies). You can go from Osaka to Kyoto either by JR West or by Hankyu. You can get from Ogikubo to Shinjuku either by Eiden or JR East. You can get to Haneda airport by Tokyo Monorail, or Keikyu. You can get to Narita by JR or by Keisei and for both of those there's a regular, and an express.
I'm sure it's not perfect but it's arguably better than many public transportation systems where the politicians underfund things and have hardly any incentive to make each station as useful and nice as possible.
The point is, there are other solutions than DC area has to have government run the transportation and all the problems come with that, at least in the USA.
Of course you have to get the incentives right. Get them wrong and it will probably be just as bad.