American Prairie in Montana is an example going the other way: a nonprofit buying private land that surround public land and opening them to the public. It's somewhat contentious locally, but it shows how much the private parcels around public land shape who can actually use it.
How does the typical suburban family look like? Did all 3-4-5 of you drive F150s there?
Other people deserve access to public land too but might not pass the vibe check of the private guards, which is what op was lamenting as well.