This sounds like a job for digital signatures using traditional certificate authority infrastructure, which has been around for decades. Think digitally signed emails or software installers… Seems like NFTs made society collectively forget about every other form of encryption.
Also keep in mind that you can only ever verify the source, not the truthfulness of the data (e.g. you can prove that the image was created by New York Times and hasn’t been altered since then, but you will never be able to prove that NYT themselves didn’t fake it in some way). Verifying the source is obviously still useful though, so it seems dumb that digital signatures aren’t more ubiquitous.
My guess is that they’ve been resisted for privacy reasons.