I also find it counter to the whole "lean startup" philosophy everyone espouses. You would think being lean would apply to their cost of living as well.

Lean doesn't mean on the cheap. It is about focusing on only the most valuable parts first. There is value in being around like minded peers. It is energizing just to be in the valley. There are millions of early adopters there. This may seem like a small thing, but it can be the difference between being eager for the next day of work or being eager for the end of the day.

If I'm not mistaken the whole concept is that any startup has a limited runway. Focusing on the valuable parts allows you to quickly test a hypothesis and pivot if it doesn't work. Living in a really expensive area is going to reduce the number of times you get to pivot.

"early adopters" of "websites" on the "internet"

you don't have to live in the bay area.