> There would also be a requirement for all playback to actually properly check the private keys
I don't think that's true. Only for someone who wanted to prove authenticity to grab the signature. No private keys would be exposed (except those which were hacked.)
If Netflix and Amazon can't keep their 4k HDR webrips from being leaked (supposedly via extracted licenses from Nvidia Shields), I have no idea how we'd expect all camera manufacturers to do it. Maybe iPhones and flagship Apple devices, but even then we'd find vulns in older devices over time.
I was thinking more about the spread of disinformation at large - but yea, that playback requirement would only be necessary for anything that wanted to be considered a potential source and trying to protect against disinformation platforms is a much larger problem then technology can solve on its own.