The maintenance on a monument will require maintenance whether people are allowed in or not. The maintenance on a sidewalk and sculptures are long term things anyways, and people don't really have an impact. Weather does. The only problem would be trash, but then again we aren't exactly evacuating D.C. and putting barricades up around the city either are we? Regardless, it would be cheaper to have someone come once a week to pick up the trash than to pay park rangers to make sure no one enters the park, rangers that weren't required when the park was open. There are some parks that would have to be closed, like pearl harbor, yellowstone, etc. But places like the WW2 and Vietnam memorial, which are open 24/7 anyways, closing them cost more than it does to keep them open.