infrastructure projects in the US tend to be really expensive and prone to cost explosions. There are a number of reasons for this- for example, the design of the terminal is absurdly overly done for what it needs to be. Another issue is regulations- we tend to build things to an absurd level of regulations. ANother issue can be environmental restrictions (these added significantly to the cost of extending BART to SFO), which are often used as obstructions to development in the Bay Area.
When you hear about massive projects being done cheaper (especially in per-mile costs), often it's because the project isn't running through an established, densely-populated area. So what you end up getting is "cost of building in a wilderness" versus "cost of building in a dense established city". The latter is going to be more expensive.
The BART extension is being built along an existing rail right-of-way for most of its distance so I'm not sure how much existing development can be blamed for the high cost.
You're right, Tokyo, Singapore, Seoul, they're not densely populated at all!
Not to say there aren't valid reasons for some projects to be more expensive (especially when you're tunneling), but by all accounts the US manages to have outsized costs for pretty much any infrastructure project.
Are infrastructure projects a lot cheaper in Japan, South Korea and Singapore? I honestly don't know. I know they have better rail infrastructure, but those societies also pay higher taxes and make rail infrastructure a higher priority.
