Yes there are a few parks out West, but the "natural areas" you mention are controlled by the BLM and US Forest Service for the most part. I feel very fortunate to live here even though I disagree somewhat with the way these lands are managed. If I did not have somewhere to roam, well I'd move somewhere else.Depends on the state and what their regulations are
Here in NY there is no collection allowed on state lands. Actually prohibited in the regulations. I've never looked into county lands but I suspect it's the same.
I think Shogun nailed the reasons. Highly populated area, relatively less open space compared to out west most of which is designated parks and natural areas