This is low hanging fruit and should happen. All devices should cryptographically sign the video and audio they record. It’s not fool proof, a state actor could probably extract the keys and forge a signature, but it would be better than nothing.
Each device should have its own key. It’s quite difficult to hack a phone, possibly disassembling it, extract the private key from hardware, reassemble the phone, and then forge a signature on fake video. Yeah, it could happen, but if it’s a serious issue the court can inspect the phone the video allegedly came from and at least for normal people, they aren’t going to be able to forge a signed video.
If we get serious about this devices could have security hardware that is difficult for even state-level actors to break.
As others have said, people will still believe what they want though. With or without fake videos and even with and without evidence.