Actually, I think this is a really great example, and how you view it says a lot about your philosophy. Let's call the libertarian astronaut Ayn. Ayn is rational, and she happens to really like breathing normally. There's no biological reason requiring her to do so, but breathing more slowly seems inconvenient to her. So she just keeps breathing normally. Since she assumes the other three astronauts to be rational, she expects them to moderate their breathing even further to account for her normal breathing.
At first, this is what happens. The other three astronauts breathe even more slowly to make up for Ayn's normal breathing, keeping them on pace for 8 hours of oxygen. But the other astronauts think this division isn't fair--there's no reason that Ayn should get more oxygen than the rest of them. They decide that they have a couple of options. First, they could all start breathing normally in the hopes that Ayn would start moderating her breathing in response. It would turn the spaceship into a contest of who blinks first, and if no one blinked soon enough, all of them would die. Second, they could kill Ayn, but they believe murder is immoral. They think Ayn's behavior is unfair, but killing is worse, so they don't do it.
Instead, the other three astronauts come up with another option. They vote on and accept the moderated breathing policy for everyone in the spaceship. Ayn refuses to participate in the vote. The other three astronauts unanimously elect one of them--we'll call him Big Brother--to regulate the use of oxygen. Big Brother keeps track of everyone's breathing and can slap people in the face if they don't breathe at the agreed-upon rate. The rules allow any three of the astronauts to vote out the oxygen regulator if he doesn't do a good job, or doesn't comply with the breathing regulations himself. Ayn might not like breathing slowly, but she likes getting slapped in the face less, so she moderates her breathing.
But now Ayn is upset. She argues forcefully that she's a bold risk-taker and that society should incentivize her risk-taking. She took a risk and breathed normally, taking what she wanted even though it created a possibility that the other astronauts would do so as well, which would kill them all. She points out that Big Brother has made some mistakes--he's miscalculated the breathing rate a couple of times and slapped people when they didn't deserve it. She argues for the deregulation of oxygen and the return of the free market. Who's right: Ayn or Big Brother? Neither is perfect, but I'll take Big Brother. The alternative is a game of chicken where the stakes are everyone's lives.
As for this example being contrived, let's change it slightly. Let's say 7 billion people are born onto a planet. This planet has limited drinkable water, breathable air, arable land, and combustible material. We can either let people use those resources however they please, risking the resources' eventual pollution, overuse, and depletion, or we can establish systems to regulate use so that they will be available to everyone for for the foreseeable future. If we don't regulate their use, we can get iPods at slightly cheaper prices, at least in the short term. The point is that people will take what they want and cut corners to make money, even if endangers the health of the human race. Yes, we're all in it together. Personally, I'll take the sustainability of the planet over cheaper iPods.
This doesn't mean that I think the government should regulate everything, that all regulation is good, or that our current system of regulation is optimal. But I think it's inarguable that some things need to be regulated, and that there is a role for government. Can government be inefficient, corrupt, or just plain wrong? Sure. It's fallible, just like any human creation (including private entities). But we need it.