It doesn't appear these closings need to make sense, they just need to be visible. Like the park on federal land that has no federal personnel or funding, but was forced to close anyway.
The Great Pretender is all about image, creating perceptions based on lies. That's why he hid the details of the ACA for four years. That's why he won't negotiate to end the shutdown/slimdown/whatever-you-want-to-call-it-down, and then lies about such negotiation being "unprecedented." That's why the Republicans -- love 'em or hate 'em -- have to win this fight. If they don't, we will have a dictator (as though we don't already have one).