Sony has stuff like this in Japan
http://www.jp.playstation.com/ps3/torne/
http://nasne.com/setting/index.html
Even streams to two Sony devices at once if you like.
So ya I don't see why can't PS4 do it if they design around it.
Tourne doesn't work for all games. Nasne is a network server-based Tourne but I think the bottleneck is on the PS3 side. So it should have the same limitations as Tourne.
I don't think live streaming is anything a console in this generation can (and should) do due to the variables and configuration details involved.
Live streaming involves a lot of customization, mixing, etc. that each streamer wants that simply cannot be done if you don't have another PC doing the work.
Any live streamer today will probably tell you that having the console to live stream by itself is quite dumb and they'd rather bring in a capture card and go from there.
Even while playing on iOS, we felt the need for game spectating. We don't want a host babbling while spectating though.
Something to stream the data to another small hardware for record and spectating would be fine for us.