Question re. div element

The HTML specs (section 7.5.4) state that
"The DIV and SPAN elements, in conjunction with the id and class attributes, offer a generic mechanism for adding structure to documents." [1]

I note that style can be added to  div so that one can be distinguished visually from  another div.

Question:
The use of div does not really convey any structure to a screen reader user. Screen reading software do not identify div in the way  they are able to identify other structural elements like paragraphs, table, list, headings and so on.
So is this a failing of screen readers or am I missing something here?
Thanks,
Sailesh
[1]  http://www.w3.org/TR/html401/struct/global.html#h-7.5.4