I thought of this as well, but its not as convenient. Even if they clipped the Vita above the controller like this...
http://www.gamestop.com/ps4/accessories/ps4-dualshock-4-controller-smart-clip/112598
The vita would be a bit too heavy. A peripheral would be ideal.
^ Also In reality, streaming from ps4 to a phone clipped onto the ds4 like in the link would be the most comfortable. Especially a phone with a large screen. Not sure if that could ever happen though.







