There's far more to see outside of those national parks and forests than there is inside. Look up any paragliders or bush pilots on YouTube that live near federal land, and they pretty much go wherever they want to go.
If you're an avid hiker or camper and are visiting the US, find local documentation on where to visit or befriend someone in the area who can make recommendations, and you'll get to see our natural landscape without all of the tourists or regulations. You can legally BASE jump off a cliff, hike in the nude, mine for gold, set up an impromptu gun range, and camp there for a couple of weeks, or indefinitely if you hike two miles each day.