Yes yes, yea of the americas with ample elbow room. Unfortunately in Europe there is mainly 2 areas, one where there are people and one where there are pointy mountains. The pointy mountains are a problem because re supplying food is a hike in itself, you cannot carry food uphill very well, by the time you get uphill it's time to come down again. The other areas it is hard to be more than a mile from a dwelling. There are areas that are more remote but they see a lot of visitors so there is control of camping to lessen the impact.

I do not know whether it is like this in the states, but here in the UK footpath erosion in some areas is a major problem due to the amount of visitors. The US has roughly the same area protected as national parks as the entire land area of the uk.