The alternatives are grim. As an extreme example, if I were to stream video to your browser from my website, evil.com, I would have to either host or proxy tho

The alternatives are grim. As an extreme example, if I were to stream video to your browser from my website, evil.com, I would have to either host or proxy those streams through my server. Instead, I can just point your browser to a video from youtube.com or something. If youtube.com then decides you need to log-in (or be logged-in) to verify your age (as they do), then that is between your browser and youtube.com to negotiate -- evil.com never sees your credentials.