[S]creen readers need to become speaking browsers: they need to ignore how the page is visually displayed, and read the content. Use semantic markup when it exists, and otherwise [...] ignore the non-semantic markup and read the content. I can accept that might fail in many cases, so I’ll present a fallback: DOCTYPE switching. If a document has a DOCTYPE that would put a visual browser into standards mode, then be a speaking browser. If not, then be a screen reader.
Amen to that. Somehow this needs to happen. It would require building a browser up from scratch, but as it wouldn’t have to support any CSS (other than voice-specific properties) my guess is that it wouldn’t be anywhere near as difficult as building a visual browser. But who’s going to build it and how would it integrate with existing accessibility software?