I think signing is a particularly weak approach, but we're going to see other tech advances to handle this problem. And I think you're right about the biggest problem: trusted sources were fine before photo evidence and will be fine without signing, but what we're going to miss is the ability for arbitrary people to provide trustworthy accounts of events.
The classic example of a tech fix is a hostage taking photos with the day's newspaper; it's a way to specify an oldest-possible date of a photograph. Similarly, you can prove that a video is not newer than some specific time by publicizing a hash of it. After that, format conversions, rehosts, etc. are all believable as long as they can be traced back to the same-hash original. And until deepfakes reach realtime speed, any specified-time event like a politician's speech can be authenticated just by posting a hash immediately after it ends.
That isn't a full solution to authenticity; a video of some unexpected event could always have been prepared in advance. And trusted-third-source verification is tricky; I'd mostly believe a Periscope or ACLU Mobile Justice video is being shot live, but uploading a pre-faked stream to the service is hardly impossible. Even there, though, I expect we'll see technological solutions. Apps could issue steganography (or other directions, like when to set keyframes) to the client as they record a video, so that pre-altered video won't update the way it's meant to. And I'm sure a lot of other options exist also.
It's going to be an interesting time, but I think we'll see quite a few clever attempts to preserve both anonymity and source-independent trust.