A key weakness of TUIs is the complete lack of accessibility. Everything is characters arranged for the eye to see, there's nothing at all for screen readers to use to extract semantic meaning.
Presumably command output with no chrome at all (only text content) would work well in a screen reader. So, I'd think the most accessible thing (today) would be to have an escape hatch to strip the output to its bones. Someone else who knows more about accessibility may know more though!
Very true, I don't even know how it would be possible without OCR that's "smart" about regions or a universal library in use that presented a way for software to see "what's going on" (pretty much a DOM equivalent)
I'm having trouble imagining how to solve this in the terminal itself—there a way to pass information to a screen-reader via some kind of side channel?
Terminals are GUI apps. In theory there could be a protocol for telling the terminal everything it needs to know for accessibility, and then convincing all terminal emulators to actually implement this, but it sounds like a nightmare.