My knowledge of screen readers is woefully inadequate, but I remember @Stomme_poes saying that commercial assistive technology can be very expensive, so people are often stuck with old versions (which, I believe, also locks them into using old browsers) because of the cost of upgrading. Whether we're now at the stage where at least the vast majority of AT users have modern versions, I don't know. Hopefully, somebody else can provide more information.
However, accessibility is about more than screen readers and assistive technology, just as disability is about more than visual impairment. Unfortunately, this fact seems to be overlooked by many, despite the fact that there are accessibility issues which are very much the responsibility of the site designer/developer.
Basic design issues such as colour contrast can affect those with poor vision or colour-blindness. There are various online tools for testing, such as https://webaim.org/resources/contrastchecker/. I use the Colour Contrast Checker tool from the Paciello Group, which also includes simulations of the effects of colour-blindness and cataracts. (The Windows version runs on Ubuntu using Wine.)
Not everyone uses (or can use) a mouse, and including keyboard accessibility should be standard. Many designers remove the browser's default outlining of focused links, but don't provide an alternative, making it hard to see where focus is on the page. Using
:focus in addition to every
To ensure accessibility, use either a device independent event handler (one that works with both the mouse and the keyboard) or use both mouse dependent and keyboard dependent event handlers.
Moving images can cause problems for some users. Again, it is the responsibility of the designer and developer to follow the guidelines and ensure their pages are usable. https://webaim.org/techniques/images/ It's not about omitting this type of content; only ensuring it's presented in a way which doesn't make the page unusable for some.
Text against a background image can be hard to read for those with visual or cognitive problems. Links which are too small and/or too close together can pose real difficulties for folk whose fine motor skills are impaired ... The list goes on.
Most of these issues have a fairly quick and simple remedy, but it needs the designer/developer to be aware of the problems and build with them in mind. https://webaim.org/articles/ provides good information on many aspects of accessibility.
Remember, too, that "disability" is not necessarily something "fixed"; the world is not divided into the able-bodied and the disabled. Anybody can acquire a disability as the result of accident or illness, and it may be permanent or temporary. Many folk with difficulties don't regard themselves as disabled at all. I have an elderly friend with severe arthritis in her hands (makes using a mouse difficult), colour-blindness and (temporarily) cataracts. She doesn't regard herself as in any way disabled, but she's a great test subject for website designs.