For context on what the OP means by "this makes the document structure completely flat to screen reader users", I highly recommend this video. It features a blind web developer navigating websites which do and do not make proper use of headings:
I would take it a bit further and ask all web developers to try to use your own site with a screen reader and turn off your monitors. It's quite an experience. For Windows, use JAWS, for Mac, use Voiceover (it's free and embedded to Mac OS)
It is, but it is mostly meaningless unless you are willing to spend a lot of time doing that and thus coming closer to the true experience of the blind users.
http://www.youtube.com/watch?v=AmUPhEVWu_E
It literally changed the way I thought about web development and accessibility.