Interesting question. I have the distinct feeling that a lot of html coders (including me...) sometimes want html to be xml ;-)
I don't agree. As has already been mentioned, it's quite clear that the w3c's opinion is that using generic elements with classes is a way of marking up content in a meaningful way.
This relates to the question I asked in the poetry thread and in my 'heavy markup' offshoot thread: why worry about the 'semantic' aspects of markup at all? The only reasonable answer I've been able to come up with (aside from 'hygenic' considerations...) is that it's potentially useful in case the content in question will ever be transformed, mined or otherwise repurposed using dom scripting, xslt or similar or in case it is expected to be accessed using different kinds of useragents.
Provided that I haven't overlooked anything obvious, I think this suggests that <div class="serial blue-widget">123456</div> is at least meaningful enough to work as well as a dedicated '<serial>' element.
I think that when we take this line of inquiry, we wind up asking the question 'if such markup is not meaningful in the same way as a specific element, what is the relevant difference? E.g. why is one meaningful and not the other?'
I think there are very good reasons for thinking that the way the authors of the html 4 specs thought about paragraphs was in a more or less purely typographical way; to repeat an oft-used example, if a paragraph is a unit of meaning, then it should arguably be able to contain an un/ordered list (at least there is nothing about an un/ordered list that I'm aware of that should prevent its belonging to a 'collection of sentences').
On the other hand, if a paragraph is a simple typographic construct (some arbitrary number of words followed by a hard return), then the <p> element should behave pretty much as it does -- and I have to admit, that I think <p> in html pretty much is or is almost '...not a semantic element at all'. If it is a 'semantic' element in the first place, it's nowhere near as rich in that sense as any of the lists or even the address element...