You've just repeated one of the largest American fallacies. People can't reinvent themselves anymore than they can leave the past behind.
Immigrants to America may well have escaped some problems but most learned that new and larger problems awaited them. A few did become obscenely wealthy but many were mired in an even greater poverty than they experienced in the old world. In many ways these new Americans became more oppressive, more racist, more class conscious than the societies they left behind.
In my extended family tree, it's mostly those who did stay behind that ended up going the furthest. Running away is never a means of solving problems.
This escapist legacy has led to the disposable society that is America.
Your reality is different from mine. I don't think that the ability to reinvent yourself is an American fallacy. Here is what I know of immigrants reinventing themselves and coming to a better place from where they left, here and now.
My first hand experience with people and families I personally know who have come to this country counters your belief that people can't start anew and purposely leave their past behind. Some people don't have the luxury of keeping a hold of their past. They may hold on to parts of their heritage like foods and celebrations but they have reinvented themselves and have become staunchly American leaving their familar world behind because they had no choice.
1. My neighbors growing up were Italian immigrants from Sicily. They forced their children to speak English and be as American as possible in order to fit into society. After just one generation their children no longer speak Italian nor have they ever returned to Italy. They are part of a larger Italian American community here with little or no ties to the old world. If they had stayed in WWII ravaged Sicily they would have starved to death. In fact their village no longer exists.
2. One of my best friends is Cuban. His family escaped Castro's revolution where all their land and businesses were confiscated and his father imprisoned. His father had a choice of leaving the country or being executed for treason. The entire family was able to escape to Miami and later to California where his father trained fixing jet airplanes and eventually became a proud American. They have absolutely no desire to go back to Cuba nor do they have any ties with that country anymore.
3. One of my college roommates was from North Dakota and his grandparents were ethnic Germans in the Ukraine. They had emigrated before Stalin's terror in the Soviet Union. If they had stayed in the Ukraine under their resistance to communalize farms they would have either starved to death or put to death by Stalin. Most all of their relatives who stayed in the Ukraine perished.
4. I went to high school with two Vietnamese friends who left in the final days of Saigon. They are both quite successful engineers in Silicon Valley now. Within one generation they went from abject poverty in Vietnam to becoming productive upper middle class citizens. They both married white ladies and have multiethnic children. They are for the most part completely Americanized and no longer speak Vietnamese.
5. A carpenter I've worked with is Bosnian. He has come here as a refugee, learned carpentry at a community college and started doing odd jobs here and there while on welfare. He and his wife after being in this country for 6 years have bought a house, owns a contracting business employing other Bosinans and Romanians and doing quite well in the building boom these last few years. They have a child now who is bilingual and seems like any other American kid. Their village in the former Yugoslavia was destroyed. Do you think they ever look back?
These immigrant experiences are not rare, in fact they are the norm from my experience, people reinventing themselves as Americans. Perhaps where I live here where multiculturalism is the norm and people can easily see through bigots their experience may have been easier. They do not see themselves as foreigners or refugees but rather as Americans first and foremost. They are eternally grateful to be living here and grateful of having the chance to "reinvent" themselves.
I don't find any of them particularly racist, oppresive or class conscious. They are only class conscious in the fact that they strove to become self sufficent and don't want to remain in the bottom rung of the economic ladder. Most immigrants I know in America are doing better than if they had stayed in their repective countries, from Finland to Mexico. They are in no way mired in greater poverty than where they came from.
My Irish ancestors probably would be dead if they had stayed in Ireland during the Potato Famine. No amount of discrimination they met in America and racist Irish American society they became a part of can compare to starving to death. They didn't run away from their problems as much as being forced out and forced to leave their past behind.
Regarding racism... you are terribly naive to think racism in America is worse than any other place in the world. Multicultural America, although not perfect is trying to become less racist and doing something to integrate people into our society. Try being a Muslim in France, Korean in Japan or a White guy in Botswana, where there is little hope of you fitting into the larger society. No, I would say there is definitely less racism in America than a place like France, Japan or Botswana, countries where homogeneity enforces institutionalized racism and culture.
Your generalizations regarding the immigrant experience ring empty for me.