I'm actually building in something similar to what you suggest, I'm calling it party mode.
Basically you pull up Rap Coach on any device, enter party mode, and then a party URL is displayed on the interface. Anyone can go to that URL and pick a beat and topic and add it to the playlist. At the end of each song it announces the next person.
So kinda like karaoke without needing a KJ. We're planning to host live Rap Coach events once that's in place.