Thanks everyone for your contributions! I think I get the specificity issue now; thanks -- it's a tough one without access to the browsers at a lower level, I fear. This is a reply specifically to @Jesse_Donat...
<hn> elements do impart meaning, and in a HTML4 setting, where they're the only semantic "structuring" elements we have, they're vital. However, if you're already using HTML5 sectioning elements, then the document structure is already imparting that meaning, so we see using
<hn> elements in HTML5 as a violation of DRY. Also, what if content is dynamically brought in from another source to form part of a larger page -- the heading structure may need fixing in order for it to fit in the master document's outline. If we have a universal heading element, it will fit in with the structure of the document in which it finds itself.
As accessibility folk, we often see incorrect document outlines -- e.g. where heading levels have been missed, or headings are using in a way that doesn't match the visual appearance of the page (sometimes people use the heading levels simply as a way to ease writing the CSS, not as a means to impart the relative importance of sections).
<html5-h> is an attempt to bring a universal heading element (such as that proposed for XHTML2 or that found in DocBook) to HTML, in recognition of the document structure defining the semantics.
I hope this explains our rationale, even if you feel that heading structure should take higher precedence than document structure.