The way we view our parks is a bit different. Our parks are pretty open and unmanaged. They're also run by multiple organizations (town/county/state) without real authorities behind them.
Parks like Dupont are destination places with a real controlling force behind them. When that organization closes the trails, it's a big deal and people listen. They have rangers that may ticket you. Only park like that around here I can think of like that is Noxamixon.