Most people in the 19th century were more independent and self reliant than today. That was the nature of life back then.
Family and church were the primary institutions of support rather than government.
As far as homesteading is concerned, there are many issues involved. Much of the land available for homesteading wasn't really any good for farming, at least not with animal power on a mere 160 acres. In the LH books, "pa" somewhere makes the comment that the land is better suited for grazing (I think Ladypine knows these books by heart
). People were already moving west for other reasons such as mining and ranching. It could be argued that the Indians and cattle ranchers had a better claim on the land than did the USG just based on prior usage.
Homesteading is glorified, but really it was bad policy. It tore the guts out of natural grasslands, which are much harder to regenerate than "old growth" forest.