I believe the Arizona National park?? Or something...was to be closed in the last closedown..but the state paid themselves to keep it open...Seems to me there's your answer...Should it be National if it makes so much in the tourist trade...or if the state can keep it open or a private business...as they did there...why do the Govt own the things and not just licence them out maybe to something like National trust over here..Not a govt dept.
It's all political theater of course. National Parks are mostly stretches of wilderness, so closing them is merely shutting down an access road and then manning it so people can't pass, instead of manning them to collect the entry fee. The WW2 Memorial is outdoors along the National Mall. It actually costs much more to put up barricades and man them than to just allow people to walk through the area as they normally do.
http://www.bbc.co.uk/news/magazine-24357415 US shutdown: 10 unexpected consequences 1. One person maintaining the Canada border 2. Cemeteries in Europe are closed 3. Sanctions respite for Iran 4. A meat rush in Kentucky 5. That race you've trained a year for... it's off 6. More James Bond buffs 7. Free food for civil servants 8. Satirical T-shirts 9. Cancer drug trials on hold 10. British people now know what 'furlough' means