XKCD has covered part of the reason: https://xkcd.com/927/
And the other thing you mention, signing data, is only as good as trusting the author themselves. Let's say there's a contentious video and it's cryptographically signed by Stefan Mousetentacle. Who is Mr. Mousetentacle, and why do we trust that he actually took the video, and didn't generate it?
https://contentauthenticity.org.
I haven’t used it, so I don’t know how good it works, but they claim tooling supports a fairly large set of file formats. See https://opensource.contentauthenticity.org/docs/c2patool#sup...