the OP pointed out that this only works if he uses a browser monoculture
the OS does have more information than that, it can know what is being played by any/all apps, and what is being picked up by the mic
fwiw, you only need to know anything about outputs if you are doing AEC. Blind source separation doesn't have that problem and can just process the input stream.
Even if this is true, it's easy to imagine such functionality being exploited by malicious apps as a security and/or privacy concern, particularly if the user needs a screen reader.
It definitely makes sense for the operating system to provide this functionality.