Wilderness is a special designation, different from public lands, national forest, state parks. It's one of the last places in the US where you can be close to being free. Public lands often border private property. National forests have strict rules on usage and have roads paved through them like theme parks. State parks often require fees for entry and design areas for easy camping/eating/leaving waste.

Wilderness areas are a "part of society." But wilderness is an idea as much as it is a place, and the only place you can engage in the idea of "wilderness" is in geographical wilderness.

Your statement suggests that the rules of domestic life should apply in wilderness, but it's our domestic laws that say that there should be some territory where the spirit of domestic life doesn't prevail.