It's bigger business for The Playstation brand to get people to buy the console and sign up for PSN though.
That is what I mean though. Have a dedicated Twitch.tv app that allows you to view streams and to stream your gameplay for everyone to see. Sure, it just means there will be tons of streams of crap gamers, but it would be a great selling point for those interested. Currently, in order to stream console games it requires additional hardware (capture card and a PC). This is something that could be removed via the console itself.