The fact of the matter is that the seeming irrationality and inefficiency of American government is a feature, rather than a bug. The inefficiency and general waste in government affairs actually serve to obfuscate the real functions and purpose of the state and makes reform vastly more complex and costly than it otherwise would be. The example I like to give is the tax code. The income tax started out as a tax on wealth and it used to be that only a very small percentage of households paid anything. Over time though, the burden of taxation shifted downward onto the middle class, while the elite simultaneously found alternative means of storing their wealth to avoid taxation almost completely. The problem is that the tax code is so complex now that most people cannot even comprehend the amount of loopholes in it. The only people who can are tax attorneys working for corporations and the ultra-rich. This is what I mean by the inefficiency and general waste serves to obfuscate the issue.
And the funny thing is, this is all working exactly as intended. The wealthy tightly control the system and the rest of the population is too distracted fighting for the crumbs to actually organize, form meaningful alliances and fight to change the status quo. What they do instead is share news articles and memes on Facebook and sign silly petitions on the Internet to be able to pat themselves in the back for fighting the good fight. They just want to feel good about themselves.
At the end of the day, this is because the vast majority of people don't actually care about the events that happen around them. They care about their self-perceived role in those events and their own feelings. You can actually see this type of behavior in many different cases outside politics. Take something as simple as exercise. A lot of people sign up for personal trainers, not because they actually want to exercise correctly and lose weight, but because the act of making superficial effort (such as paying a small amount of money) towards a goal is sufficient to make them feel good. And if they fail at weight loss, they can tell themselves that, well, they at least tried. Which is what the signers of this petition are going to tell themselves when it accomplishes nothing.