It's not clear that there's really that much demand for captioning. There's a CA law that's created a perverse opportunity for aggrieved individuals to try and extort money out of public institutions who put content online; it's not clear to me that they represent a bona fide constituency in need of captioning. (I'm sure that such a bona fide need does exist, but I don't think the people pushing Berkeley in this case are it.)

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.