The reason they are administered Steve is to ensure that these areas of outstanding beauty are protected from being ruined by being over visited and having wildlife and their habitats destroyed, and the landscapes that the public come to see are not covered with camp sites, cars and litter etc..
I appreciate that and it is good that it is done but closing them would appear to be an impossible (if not illegal) task for our UK parks. Not sure about the US parks but they must be accessible by means other than by road so it is probably also very difficult to fully close US parks too.
"People who say things won't work are a dime a dozen. People who figure out how to make things work are worth a fortune" - Dave Rat.