I'm not sure the prosecution part is as important as the public's image. The fact is that someone can ruin your life with a fake video, and the tools for doing so are becoming easier and faster to use. Regardless of if the court believes the video or not, your social and professional life could already be ruined by the time they view the video.
No. Adding cryptography to video recordings is the worst of both Canudos. It can verify sources but not the literal truth. All that would do is half-mirror society where any ole bullshit signed by the credible is accepted while man on the street police brutality or politicians making out with a 12 year old are called fake.
I've seen many an up close magic trick in person that I've been unable to figure out. In person only prevents digital shenanigans, not _all_ shenanigans.