What I can tell you for sure is that most sites are accessible to the extent that HTML makes accessibility the default, and the instant people start doing stuff

What I can tell you for sure is that most sites are accessible to the extent that HTML makes accessibility the default, and the instant people start doing stuff that's not accessible-by-default (JS checkbox widgets, for instance), it almost always gets ignored and dropped. So when you start talking about ignore-the-DOM stuff, my strong suspicion is that it would all be completely and totally inaccessible.