Recording a hash of a video in the Bitcoin blockchain creates public evidence that the video existed at a specific point in time. If that point is very soon after the events portrayed in the video then it can increase confidence in the video's authenticity.

Proves nothing about authenticity. Requires an internet connection which means in many cases it's completely impractical.

I think it would be more like prior art, to distinguish originals from copies rather than to authenticate the content itself. Given two pieces of similar-but-different video the one with the earliest timestamp is presumably the original.