You make an interesting point that made me realize something.
I already pay for a couple of (digital) newspaper subscriptions, but I am willing to pay double that (if not more) for a subscription to a news publication that explicitly prohibits their writers from using tweets as sources or evidence of anything in their coverage. I am very sick and tired of how often "news" is not actual news, but a "journalist" trying to pump out articles and harvest clicks by just searching for whatever tweet to make a point they want to make seem as "real" in the article. Imo people gossipping online isn't the news I want to read, and a sample of a few randos tweeting something that supports your point is not valid data.
Rare exceptions apply where the tweet itself counts as material news, e.g., it was made by a leader of a country and it actually is some big news and the tweet itself is being the primary source (e.g., not just a link to an official press release). But it is so rare, it could be imo almost discounted. Also wouldn't apply to video footage sourced from twitter, because a video is a video, regardless of where it originated.