I don’t doubt it, but I do doubt that the majority of the public will make an effort to verify signatures before consuming media. I think the public will rely on trusted channels - like the personality’s .com or official YouTube channel.
Yeah, I think it would have to be handled in the player. Similar to https, it would warn you if the stream isn't verifiable with a known key. You'll still be able to consumer unencrypted streams, or streams whose key isn't from a recognized authority. but you'll get a warning.