There will be lots of good reasons for a video not to match bit-for-bit from CSPAN- if I add commentary on top of it, or intercut it with other clips Daily Show style, or just re-encode it, the hashes won't match. False positives are the death of an indicator, and there will be far too many of those for this sort of scheme to work.
The issue here is that there is no trusted authority on the video, the people distributing the video are the content originators so we can use a signature to verify the video wasn't corrupted in transmission but not that it wasn't edited before it was signed.
(this technique would work well if the concern was that videos from some primary source were being edited by a CDN entity helping to stream that video to viewers, which is entirely separate from the article)
Assuming you got it to work sanely, how would you ensure that all manufacturers properly locked down their devices?
Assuming there's a reasonable trust framework and you're able to enforce it... How would you allow legitimate video editing without allowing people to edit video to create misleading images? How would a movie cut between characters and an exploding model in a legitimate and signed manner without allowing someone to splice a politician's speech in with terrorist training videos?
There is a lot wrong with this "Tech can fix it" approach.