Protest brings people together. When it's a small protest, it's like a convention for the chronic opposition. But when a protest starts bringing in more attention, it brings people who show up in contact with new ideas, and creates a fertile ground for new collaborations. This happens in big ways (the idea of the 99% and the public understanding of accelerating wealth gaps owe a lot to Occupy, and the Bernie campaign is pretty much a direct consequence) and in smaller ways (Occupy led to many people switching from standard banks to credit unions, and also led to some excellent work opposing predatory student loans).

When you sit back and let the protest burn, you risk allowing the discontent to generalize and grow. But, sure, maybe it will just fizzle out, if there is still enough bread and circus to go around.