If they streamed videos with no-DRM, everyone with a subscription would easily grab a copy of whatever they want. And all it would take is copying a file and sharing it with friends/family to have it spread. This might not seem like a huge difference, but honestly I think it would be. It would lower the barriers of sharing to the point that everyone could do it. Only those who hold onto a moral belief in not committing copyright infringement wouldn't participate. I think the past has shown that these people are in the vast minority.