Firefox and Chrome both have mature accessibility API implementations at this point. Edge is also at least okay. Internet Explorer has worked forever. You then couple those with a screen reader--most commonly Jaws or NVDA--and you get something that very much resembles Emacs or what have you: there's around 50 or 60 keystrokes I use on a regular basis. It's like a local client-server model (indeed documentation on this topic uses those terms). You couple something implementing the server with a client, i.e. a screen reader, a one-switch controller, speech recognition, what have you, and those consume exposed semantic information. Browsers then map web pages to the platform's accessibility model for consumption.

NVDA offers scriptability for the web and otherwise in Python as well, so anything it can't do can probably be added. For instance there's an add-on for using your local screen reader to control a remote machine, provided that both run it (not the most applicable to accessibility, but a good example of how far you can take NVDA's scripting). Jaws also does much of this but is much more proprietary including an only half documented scripting language.

The quickest way to get some idea is to probably look at the NVDA user guide: https://www.nvaccess.org/files/nvda/documentation/userGuide....

iOS is also good. unfortunately Apple very much dropped the ball on OS X and hasn't picked it up again, but my brother (also blind, it's genetic) did an entire business degree on an iPhone because he didn't want to be bothered learning a laptop. That's a loss in efficiency, but even the lesser options are now sufficient enough that a non-programmer can pick them up and go get a college degree.

There is an idea that goes something like "Obviously screen readers have to struggle to present information, therefore dedicated text-based browsers are better". That was true in 1995 when we didn't even have MSAA. I know people from that era and they had to hook APIs in other processes at runtime. But in actuality, once you expose the accessibility tree and hand it over to the people who want to use it, good things happen.

Ah, I'm sorry, I misunderstood what you meant. You're talking about screen reader compatibility only.

I was interested in hearing about browsers that do what Lynx does, but are better. Unfortunately, the browsers you mention are graphical, and so are not Lynx replacements.

From my perspective there is very little difference. The interface I get out of Firefox is exposed as if it were a text-based browser for lack of a better analogy (it's not quite the same, but the differences are subtle and not obvious at first glance). But I also get the ability to do all the non-text-based-browser things with that interface instead of being limited to what a text-based browser supports, and those things can be made accessible to me. But the really big advantage is that my skills at driving Firefox also work with Chrome, IE, and Edge, and any web view on the platform. Plus there is a large common subset that is shared with all the desktop apps as well.

I'm not the right person if you're looking for someone who shares enthusiasm for text-based browsers, in other words. In general I would like it if people would stop using blindness as a point in their arguments that they're necessary because it shows a massive misunderstanding of what the world of accessibility is like.

In that sense, there's links2 (http://links.twibright.com/). (While it supports graphical output, it's a text-mode browser at heart.)