I'm thinking something a little less random might serve this idea better. Perhaps more or less like a room, where you could see multiple people all at once. Could make public or private rooms. I'd also almost say don't even allow web cam, just strictly desktop streaming. But, I could also see how seeing faces could be helpful, too. Perhaps it could have Picture-in-Picture, and you could swap between your desktop or you face being big, and the other being small in the corner. Some tutorial videos do this - it has their desktop with their face in the bottom right.
I just don't think much would get done if you were just on there finding people that may or may not have anything in common.