I'm not a designer (or a good one, anyway), so I welcome corrections from good designers, but I'd assume that whether or not flatness in this sense is a good idea would totally depend on context: how much site navigation is there, how many other presentational elements, ads, links to other things, etc.
Svtble works because it takes a minimalist's approach to all of that, throwing it all away into the bin. The content is readable because it's almost the only thing on the page. The font is large and the content is centered.
But would that work in the general case, as an approach for user interfaces and search engines and the modern day portal page and so on? I can't think of any examples there that would be considered "good design".