As for rel=next/previous, I don't use them because Google makes it clear that these will make it treat the whole sequence like one paginated document in the index, contrary to their original semantics. I'd love if someone could correct me on this.
[0] http://webmasters.stackexchange.com/questions/61573/is-it-ju...
[1] https://www.w3.org/TR/html401/struct/links.html#h-12.3
[2] https://webmasters.googleblog.com/2011/09/pagination-with-re...
zero gain. There is just no application. Google works perfectly fine. Give it up already.
And just to take this to another tangent.. Word won the office space. There are no normal people writing LaTeX for their party invitation. And hell, even the people writing LaTeX don't want to bother with the "machine-understandable" thing so they went ahead and made it into a proper Turing complete programming language.
Even simple stuff like asking the writer to clarify which piece of a text that a written date applies to would be helpful, and to define what parts of long sentences with many commas belong together (which subsentences are interjections, for example?).
Otherwise I'd be curious to hear how or why including web page layout semantics in HTTP would be useful.
Fortunately, we usually don't need to process web pages using fancy yet hardly accurate algorithms in order to extract machine-readable text from web pages. Why? It's because we agreed to use character codes to codify letters and most of the time text is encoded using some character code, which makes it unnecessary to OCR pictures of hand-written letters to programatically process text from web pages.
These kinds of program wouldn't be needed if only the same thing had happened for page structures, if HTTP included page semantics.