I personally prefer using <h1-6> and do not see, why always using <h1> may be better.

Furthermore I think that using <h1> in this case is quite irritating. The HTML 4.01 standard says the h1-heading to be most important, the HTML 5 standard defines it as having the highest rank. It is in my eyes unintuitive having only headings of highest rank in a document. (Yes, I know, that this isn't quite correct, but from the view of a simple html author who doesn't really care about outline algorithms, this is true.) What would make much more sense, is to omit the rank fully, so only only has to write <h>.
<section>
<h>Rank of this title is to be found using the outline algorithm</h>
<p>Yey, content!</p>
</section>

Furthermore this ensures that one can easily style a document that uses both the <section>ed variant and the <hX>-ranked one without having an extra selector.

Beyond that, using <h> instead of <h1> would even be more backwards compatible to the HTML 4 use of headings.

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