I think it's flat because it's easier to add CSS and build up widgets as opposed to having a stylized widget, then trying to override the CSS to re-customize each widget. Foundation, the original front-end framework which Bootstrap emulates, works the same way.
Foundation doesn't isn't completely flat though. Buttons, for example, hint at being intractable by giving a tiny bit of depth using the line at the top of the object.
If nothing else, it's easier to override with your own styles.
Exactly. In BS 2 it was such a pain to remove the gradients from buttons, the box-shadows from inputs and all the other extra UI effects that you didn't want to use.