Camping in this country is sometimes associated with fire rings, empty cans and broken glass, too. The leave no trace ethic has not penetrated very deeply. But trespassing is a shooting offense in some places in the U.S. Some people are very sensitive about property ownership, sometimes even if they don't own the property. But there are lots and lots of places to camp not far from where I live and with some discretion and familiarity with the area, even nude hiking, as I still do. But I wouldn't go this time of the year. Not nude, anyway. I've had some of my most enjoyable outings in the winter.
In the East, where there is virtually no wilderness, it is difficult to do any long distance hiking (and camping) without running into other people or habitations. But there are a few places, to be sure. The famous Appalachian Trail runs through well-populated areas and because it tends to follow the ridges, it's easy to see houses most of the way, especially at night. But the trail goes through or near towns, too. Can't speak for the trails out West, though. Beyond the Mississippi River, though, the population thins out. In fact, some places have become somewhat depopulated.
There was an article by A. G. Cousins that appeared in the December 1971 issue of The Scots Magazine. He described his 26 day walk from Cape Wrath to Glasgow. So clearly long-distance hiking is possible in the U.K, or at least in Scotland. I've been to England and Scotland, as well as France and Germany (lived in Germany for two years in the 60s) and I wouldn't describe those places as crowded, not by my standards. I even went through places in England that were very much like places in West Virginia. In the Eastern U.S., however, from Washington, D.C. and maybe even Richmond, to Boston, it's almost one long urban and suburban strip. It is a strip, though, and one doesn't have to go very far west to be in really rural places, though hardly what I would call wilderness. Even so, there are deer in my backyard now and then. There have been bears spotted in the county occasionally, out to see the world I guess, so it's probably only a matter of time before I see one from my dining room window. So far, I've only seen them when I was on the Appalachian Trail in the summer.