Jobs, family connections, lack of money to pick up and move. The same reasons people today stay in a lot of less-than-wonderful places, or sometimes even move from places with a better climate to ones with a worse one. Why do you stay where you are, instead of moving south?
Suppose you were a factory worker in the 19th century. You weren’t going to find a lot of jobs that you were qualified for on the frontier or in much of the South, and you might not have had the skill or desire to do something that you could do to make a living elsewhere. You might not have had English as your first language, and you might have wanted to stay where there were other people who spoke your mother tongue- learning a new language as an adult was and is not easy, especially if you’re working full time. You probably also weren’t rich. They might have been giving away land, but they weren’t giving away the wagons or horses or supplies you would have needed to make the trip.
A huge number DID emigrate further west. Most states westward to about Texas in the South were already states, territories or republics by 1836, and quite a few were already established much earlier than that- some in the late 18th century.
I think a lot of why the population wasn’t denser is because the South was primarily agrarian, while the Northeast was more industrialized. Basically, more people could live in the North than the South by the way things were set up.
I live in the area between the mountains & the desert. It is a narrow non-continuous strip of land that is much harder to travel then the desert is. There are many washes, gullies, streams, & rivers that one would have to cross. The desert will have two or three large rivers to cross instead of the hundreds of washes, etc. Most of these water courses are dry in the late summer.
If it is not full of water, the river bed is actually often the best path for a traveler to take. One must watch out for flash floods & water falls (cliffs) though. Dry, (or wet), panning for gold can be done at the rest stops if one is so inclined & has the time.