<section> once drove the model where we were going to kind of soft-kill the h1-h6 elements and have only h1s where their heading level depended on the section nesting level... but my understanding is that this didn't really work out and is functionally dead, and the current recommendations are all to just use the range of numbered headings as before.
Do screen readers use a different user agent? Seems like a11y would be simpler in many cases by just delivering a text based result that's tailored to screen readers. Most of the issues seem to arise from the structure chosen in order to style things rather than the content itself.
And just expecting that vaguely guessing what the other wants will work.
And probably some optimization on the engines to sort the fetching of the resources and painting the screen.