But here's the thing: If the shutdown had been timed differently, and had prevented me from going, I would have been okay with that. Because, yes, the park belongs to the people of the United States. But the park has rules, and those rules are for the protection of the park. I couldn't use my own money to throw coins at the thermal features, because that's destructive and not considerate of the other three hundred million people who own the park. I couldn't feed the bears, or shoot the bears.
Taking care of the national parks is a huge undertaking. There's conservation and cleanup and making sure people follow the rules. There are rangers who can teach you more. A whole range of people who have been sent home without pay. The only people left are the people to close the gates, because people have an impact on the parks that has to be constantly managed, and all those people are at home watching Maury Povich.
And the kicker is that, the people closing the gates, the ones being painted as the jackbooted thugs of a horrible dictator? AREN'T GETTING PAID. They're doing it because it's their job, and they hope they'll get backpay.
Now, consider how hard it would be for your family to miss a couple paychecks and not know when they're coming. And then think about having to go into work anyway, and then being painted as some kind of commie traitor for it.
TL;DR: You shut it down, it goes away. Even if you don't want it to.
And, yeah, the National Mall was closed off in '95, too.