This is not a new idea, but it is a newer innovation. Systems have tried to incorporate mobile video in their production switchers, but there has normally been a fail, especially when audio is involved. Switcher Studio has worked out that problem and turned their program to all mobile devices.
I first saw this program at SXSW when a one-on-one interview was being conducted. Two phones, one iPad (for switching the video content). The phones would connect to the iPad via WiFi, then the iPad would not only swap out the video, but also add lower 3rds, graphics, and pre-recorded scenes.
I grilled Switcher Studio on the latency issues. The biggest issue being lag from a phone to the audio track being supplied. I was assured that as long as audio came into the iPad via Lightning or headset, it will match the video coming in.
This is due to a delay they built into the streaming unit. It allows the phone to catch up to the audio and sync properly.
While I have a little more research to do, this might be the best solution for mobile device streaming to Facebook, YouTube, or anything with an RTMP connection.
The free version only records, but for $25/month you can turn all your old iOS devices into cameras.