Since the web came into being, there have been tools created as add-ons to change the user experience.
As early as the 1990s, overlay screenreaders were created so that users with low vision could have their browsers read the content to them off the screen.
According to SiteImprove, accessibility overlay tools are automated software solutions that claim to detect and fix web accessibility issues.
There are some simple accessibility issues that overlay tools can identify and resolve, but there are also many other critical problems they cannot fix. However, hundreds of lawsuits and millions of dollars have said that accessibility overlays simply cannot fix everything.
If a screen reader is an overlay, imagine doubling on overlays, like wearing two pairs of glasses at the same time. There is bound to be a disruption that will lead to a negative and/or incomplete user experience. No widget or overlay can magically make a website accessible.