Just because change doesn't come directly from these petitions, it doesn't mean they're worthless. They act as a gauge, not necessarily for our government, but for us, showing the amount of support that exists behind a given idea or movement. It's not precise, and is not the only gauge, but it at least functions as one piece of the puzzle of affecting real change. Your cynicism is wasted here.

> If petitions actually worked, they'd be banned.

Replace "petitions" with voting, protesting, posting comments on Hacker News, or talking with your fellow citizens about political issues. All those are other pieces to the puzzle. Why aren't they banned?