I can see a lot of the technical/privacy/security challenges with a full blown API but as someone who works with small organisational websites a lot, knowing how many screen reader users (a simple user-agent style record would be enough) were visiting them would certainly help in allocating resources and convincing people in making the right decisions. The argument that all websites should be made accessible by default (while fine as an ideal) simply does not stand up in the real world of small to medium websites. A proper accessibility audit often costs as much as the website development so companies just rely on the word of developers that they deliver ‘compliant’ (NOT accessible) websites. Most of these developers are absolutely clueless and are essentially lying but their clients don’t have the knowledge to identify the issues. And then the standard response is: ‘How many blind people come to our website, anyway.’ And at the moment, we don’t have an answer for them. I, too, am against alternative versions of websites, but even if some sites chose that option, most would probably just focus on straight up accessibility. As it stands, they’re just burying their heads in the sand. And the accessibility community is not making it easier by not giving them information. (After all, how hard would it be to add a switch user agent option to a screen reader for those who feel strongly about this.)