Sony are kind of at fault here for even giving publishers that option, really. In 2016 we're in a world where people can just pop in to peek at their friends' games on Steam, or where someone can stream any PC game with a few minute's effort, or where people who really want to stream console games can drop a hundred bucks on a USB device that'll stream an HD input from their computer. There's nothing actually to be gained from locking down the on-system streaming with this kind of restriction except pandering to self-defeating paranoia on the publishers' part.
Am I correct in believing that on-system Twitch streaming on Xbox One doesn't have the same limitation? I haven't been able to find any evidence of such a restriction, anyway, which if true suggests that this wasn't some unavoidable licensing issue.