They want you to stay home. While I'm not sure I totally agree. I do understand the logic.
Closing CG's hopefully limits activity and interaction.
Maybe if the CG if 15 minutes from home there is limited interaction.
But if your coming from faraway, you may need, fuel, food, and whatever assistance required.
Closing the CG eliminates all that activity. It also eliminates the need for CG staff and all the services required by the CG.
In the grand scheme of things camping is a leisurely activity. It is not necessary and easy to shut down. There is no requirement/necessity to keep it open. For that reason we are seeing government run CG's closing.
Private CG that have livelihoods involved are more willing to weather the virus storm and remain open, but government CG are closing,it's a simple thing to do. From a community spread perspective there is no upside to keeping them open.