Browsers do that for sites, and I don’t see how sites are different than videos in this regard. Both are information with an origin. CA already exists, only video players have to keep up. People who trust anything they see, hear or read cannot benefit from that, but why is this a concern? Politics and cheap press fooled them since forever. The only problem I see here is that the same amount of uneducated people could be fooled like never before, but the same could (and will) be done in the opposite way to overwhelm them and detract from wrong reasoning.
I mean, the entire “problem” arises not because deepfakes, but because that video thing still lives in a century which allowed “hacking” sites and owning bank accounts via plain-text “secret” queries or cvc codes clearly printed on the back of the card with no additional confirmation required to withdraw your money. That window should have been closed regardless of deep fakes.