I think we delude ourselves thinking we should be like a small European country. Much of the vast distances in the USA are not very "walkable", regardless of private property. In the East, perhaps. John Muir walked from Wisconsin (I believe) to Florida. There is plenty of BLM land to "walk across" out west, but I for one, have no desire to do it. No water, vast distances, searing heat.
In areas that are walkable, there is a movement to provide access - for example "Rails to Trails".
Unfortunately, private land owners have had bad experiences with inconsiderate people. I hardly blame them for not allowing access. It is not just liability, it is property damage, leaving gates open, poop on the ground, campfires not fully extinguished. The list goes on. It only takes a few "bad apples" to put up the "no trespassing" sign.
What we have here, is a great system of public lands that provide enough walking possibilities to last me a lifetime. We just have to fight the push to privatize public lands.