<p><span class="cut-me-first">Well, </span>yes, but <span class="essential">in only the broadest sense possible.</span> <span class="cut-me-next">For the purposes of an op-ed piece <span class="nice-to-have">or a feature story</span>, though, you'd need to have much more control.</span></p>

<p class="normal-priority">Actually, this comment illustrates that such a system might not be as easy as you'd think. Some natural-language processing/generation would come in handy to ensure the following <num-of-bullets> things:</p>

    * proper capitalization
    * subject/verb agreement
    * proper punctuation
    <span class="cut-me-first">* number agreement</span>

Aren't these the job of a human editor? (or is this the reason why my e-newspapers have so many copy editing errors?)

No. Or rather; that would be pretty horrible html from a semantic standpoint -- and perhaps more importantly, it would need parsing into text anyway -- so might as well be more explicitly different from html.

That said, html5 is pretty free in terms of what you put in the document -- personally I'd probably prefer a "weight" or "weight-group" attribute applied to elements and/or set on span-elements. Weight might be a float between 0.0 and 1.0 (pick one to be most important, maybe let "heavy" weights "sink to the bottom", and "fall off"... ?) -- the idea of a "weight-group" would be to group headers and/or phrases/paragraphs to be dropped together -- eg for this comment, you might want to drop all references to "weight-group" -- if you wanted a shorter, simpler version.

Too far down this path and you're square in natural language processing territory -- but it should be easy to mock up a web app that lets the author/editor preview how different versions would render/look -- and allow adding/removing tags/weights to the text(s) as appropriate.

Perhaps one useful extension would be auto-promoting a paragraph and/or (depending on format/space) part of a paragraph, or just a header -- to be used as a "deck" and/or summary (for eg rss feeds) etc?

You're missing the mark of this scenario — the headings are all more important than paragraphs, but maybe a summary or "background info" paragraph is clearly less integral than its nearby paragraphs, or maybe the second half of an intro feels a bit "fluffy" but still adds. If you have space constraints, they'd be the first priority to go.

Those are for headers. Hence the "h". Not for paragraphs or sentences.