Imagine if you could save a video by watching it and correcting the typos in the existing transcript.
But there's no way it'd be a viable business. (That's Rev, and it costs $1/minute, and it doesn't even give you a .srt file that you can upload to YouTube.)
Plus, you'd have to deal with spam/abuse, and creative uses of captions (e.g. niconico).
I tried building a prototype of this in college, but I couldn't figure out how to make it work financially, so I had to take a paid summer internship at YouTube.
If it has existed for years, why wasn't it used to save the UC Berkeley library videos?
I'm thinking more of a Google Docs style interface, where you can make a lightweight edit (only one or two lines of captions) and someone else can concurrently time and edit other lines.
So even though it's free, somehow they have to take it down and ruin it for everyone.