Apparently their last real competitor, Own3D.tv, couldn't make good on payments owed to streamers and closed up shop. That should be a pretty good indicator about the profitability of this business model. Twitch has some interesting exclusivity deals with Xbox, PS4 and Mojang but forced ads for a Honda Civic I don't care about on the video preroll can't be paying their bills.
Twitch is still powered by venture capital, with their latest $20 million Series C round a few days ago. No doubt the exit strategy is to reach critical mass and then unload the business onto a company that can handle the bandwidth bills + stream partner payouts.