You know, I can't say I'd heard that bit about the "empty space" before. It's kind of interesting.
But I think that might have been partly the fault of Old World diseases being brought to the Americas.
Oh, it was incredibly the fault of Old World diseases being brought to the Americas. It reduced the population density by as much as 9/10ths. Naturally, the Europeans/Americans overlooked this, noted that sometimes areas the size of entire states had less than 50,000 people living in them, and used "poor land usage" as an excuse for seizing land from Native Americans. "A white man can feed as many people with an acre of land as an Indian can with a square mile" was a settler slogan from the 1840s. Of course, as I say, prior to the Europeans having arrived, that same area may have held up to ten times the number of people.
Population loss aside, the ways of Europeans and American Indians clashed in other ways. Tribes would sometimes go on seasonal hunting trips, only to find that squatters had moved in and built cabins while they were gone. Most Eastern Native American tribes kept large open hunting grounds that could be as large as thousands of square miles, as hunted meat was a major part of the diet and the traditional food-gathering task of adult men. Women meanwhile did the farming. Shifting to European-style intensive agriculture involved a reversal of gender rolls for many farming tribes, which was no doubt another roadblock to its adoption.
And keep in mind, the American Indian way of doing things made perfect sense for the environment. They were both farmers and hunters. They didn't have heavy plow animals or livestock, so meat had to be hunted. Hunters were also expected to be warriors, and hunting honed their skills. In contrast, a European farmer, whose farm typically consists of a husband-wife team, has limited military uses, as he cannot go on a long military campaign or there'll be nobody to harvest the crops. So in order to supply any troops other than simple defensive militia, the settled farming society has to produce enough surplus food to feed professional or at least temporary soldiers, who during a military campaign are able to do nothing but soldier.