I find it hard to understand why nothing does this already, for pre-recorded media I mean, not live. For most media the subtitle track is already separate, many have it as a .srt track. Shouldn't you be able to get an app which reads the .srt track on its own and can read the on time and off time information so the captions run in time with the original movie? Then I could sit down with subtitle haters and put on a digital movie and have the video and audio tracks play to the TV but the subtitle track play to my smartphone. It seems silly that you can't have this kind of thing through a variation on Multiple Monitors software that allows you to open some PC programs in one monitor and other programs on an entirely different screen, seems reasonable that instead of always showing a direct duplicate it should be possible to stream the movie to a TV and the subtitles to a smartphone, or show a small screen copy of the movie with the subs over it and a large screen duplication of the movie but with no subs track. If someone thought there was money in it it could be done reasonably quickly and easily on digital download types of media. Physical media (DVDs, Blurays) are more challenging for how to split a signal and also retain copy protection, etc. but it's not pie in the sky.
