They close down the parks, because (even though not much money is spent there) it's something Americans will notice. Supposedly. Personally, the ONLY time I see federal employees at national parks is when they "shut down" the government. Any other time, you want to talk to a ranger or whatever - they're nowhere to be found.
it isn't just the parks and museums that are closed ( it IS shutdown already)-it's also the FDA who inspects your food and medications, and the CDC which investigate communicable ( and dangerous) diseases,and the EPA that makes sure your country is environmentally safe. It IS a big deal-for EVERYONE