Here is an amazing opportunity for somebody "independently wealthy" to make a real difference: set up a fund that pays for close-captioning of any free content coming out of Berkeley.
Transcribing every video might be a terrible use of resources, unless there are other benefits of the transcripts (which might be the case; search would be a nice side effect).
A better solution would be to allow a user to request a captioned version of a video and then have it farmed out to volunteers. It would be a much more reasonable amount of effort (with some ratelimiting to prevent asshat behavior or scripting) and you'd be sure to transcribe the content that users actually want first. By chunking a video up, you might be able to transcribe it quite quickly, too. If I did need video captioning, I'd much rather have a system like that, vs. hoping that some multi-year effort to transcribe everything has hit the one video I need today.
However, it's not clear that such a solution would actually help Berkeley, because of the asinine way the laws are written.
Is this idea feasible?
P.s. Your idea completely makes sense. I wish google instead of wasting money in many different ways(for example starting cs education site , which of course will be not even close to what Berkeley offers) would do this. Anyone would do this ,would become my here, literally.