Twitter just added the ability to add alt-text to images in tweets thereby making them screen reader accessible, but you have to opt-in to use this feature. From the announcement:
Enable this feature by using the compose image descriptions option in the Twitter app’s accessibility settings. The next time you add an image to a Tweet, each thumbnail in the composer will have an add description button.
Now here is a quote from the blog post announcing the algorithmically sorted timeline:
…we’ll be turning on the feature for you in coming weeks — look out for a notification in your timeline. We love it and think you will too. If you don’t, send your thoughts our way, and you can easily turn it off in settings.
So a user has to opt-in for accessibility, but opt-out of a “feature” that breaks the core value proposition of the service.