We've had clients assume the Add A Comment box at the bottom right would timestamp their listening position similar to how Dropbox does for audio, and we ended up with a bunch of notes without timestamps. To be honest I also assumed that box would be timestamped.
I'm not sure the use case for document-wide comments but I'm sure someone likes being able to do that, but I definitely don't think it should be the default when every feedback platform that shows a box next to a media player makes that comment timestamped to the playback position.
I think my ideal would be a timestamp appears by default when you click to add a comment, and you could backspace it if you wanted to