If you're goal is to be an advocate for liberty, I'd suggest that this isn't the best way to respond to such arguments. You're trying to convince people, not berate them.
People who claim the necessity of government do have substantial work behind that claim. You might end up rejecting their arguments and evidence--as I ultimately do--but what they have to say isn't nonsense on its face, and these aren't gullible people.
I'm not saying you're wrong, in the end, but the people who disagree with you aren't stupid, they aren't dupes, and wrestling with and taking seriously what they say, in the best versions of it, is demanding, but it's also the only way we libertarians stand a chance of moving the world in our direction.
RE: Libertarianism can and does work