I'll grant some of what you're saying, but MANY phases of settlement by US folks (or colonials) were cases of people knowingly stepping out "beyond the pale", beyond the accepted boundaries of the colony, state, etc. Most of the people who did felt that they could simply fend for themselves against natives, robbers, animals, etc. Quite often, then, the government "caught up" with the new reality that there were people living out there and moved their accepted border to (again) encircle them.
And yet the population of the West was about zero until the railroads came, with only a handful of exceptions like in California. So, okay, if gold is discovered somewhere, people will rush there regardless of whether there's a functioning state. That's not a specifically American feature - Canada had gold rushes, just like the US. That's why Yukon separated from the Northwest Territories.
Even your point about mine owners "becoming their own law" demonstrates this -- they went to where there was no established law and set up their own systems (guards, etc) to defend their claims.
That's not really what happened, though. What happened is that powerful people bought the law. For example, in California, the Gang of Four controlled the state in the early Gilded Age. It didn't create the state or set up its own system where there was none; it took over the state using money.
That is certainly true of the latter half of the 19th century, but beforehand, the government control of settlement was scant at best, and this led to things like Texas and California overthrowing the Mexicans and declaring independence, as well as all of the violence and strife that stemmed from the fur trade.
The settlement of Texas was very far from rugged individualism, too. It was a concerted effort by the Southern plantation owners to expand slavery to the west, secure in the knowledge that the federal government would soon bail them out, which it indeed did in going to war with Mexico. The Texians did not invent Manifest Destiny. The instigating force was civil society rather than the government, but it's still not the same as the image of the lone settler bringing civilization to the west.
As far as the Indians go, their population was so diminished by the time of actual Western expansion (modern estimates indicate that at least 90% of the population perished from disease in the centuries dating from first contact with the Spanish) that actual Indians wars were more of an invention by American moviemakers than anything else.
That's completely untrue. First, it's not really true that modern estimates say what you think they say. There's an ongoing debate between high and low counters about the population of the Americas in 1492; the numbers converge by about 1600, and if you believe the high counters, there was 90% population loss in the 16c, largely from disease.
However, there was still a sizable indigenous population in the Western US that survived to the 19c, and was wiped out then. For example, California went from 300,000 people when Spain started settling it seriously in the late 18c to 100,000 on the eve of the Gold Rush and then to 25,000 by the early 20c. This was not about virgin soil epidemics - unlike in the 16c, there were enough white settlers to kill off the population, with documented acts of dispossession, wars of conquest, bounties established by states for Indian scalps, etc. In the Plains, there were Indians until the railroads came, and ethnically cleansing them from where white people wanted to settle required bringing in the Army, repeatedly.