Your thesis has holes in it. Some remnants may have teeth. But not all.
My wife is Chinese-American. She and her five siblings spoke only Chinese until they entered public school as 5-year-olds. They still speak Chinese as well as perfect English. So no, after Asian children are born in the USA, they don't necessarily speak English with no accent right away. Many enter public school in confusion until they pick up English by association with others. And a lot of Asians didn't come here just to work the railroads. A lot were sailors or workers who came to work farms or do other work. Some of that had to do with racist policies in play. When there were restrictions or outright bans on one race, say Chinese, then employers brought in Japanese. Then Filipinos and so on. Not all were in ghettos, as many were farm workers. A big example are the Japanese, who converted unusable land into rich farmland in California's central valley, only to have it taken away when they were sent to concentration camps.
As for African-Americans, they had it the worst. Many want out of the ghetto, but peer pressure is strong. I have well-to-do black friends who lament that their grown kids want to hang out with ghetto kids and they mimic ghetto talk. That's a tragedy.
I have watched several Chinese and other Asians try to keep there children speaking their own language. But often they loose the battle. The parents speak Chinese at home but as the children get older they start to only hear Chinese but speak back to their parents in English. If the parents work in an English office they become fluent as well, but often with a heavy accent. The kids lose their accent or not depending on their school friends (and number of siblings). If their school friends all have similar backgrounds they can keep their native tongue longer. But if not they lose their accent and soon lose their ability to speak the language well, even if they can understand it.
I’m guessing your wife was in a Chinese community here. With Chinese friends at school and maybe Chinese Sunday School. The large family helps keep the language and if the mother works in an environment that only speaks Chinese she will be less tolerant of English spoken in the home.
Anyway the Chinese will separate your wife as not being one of them. Go to Shanghai or Xian. Banana, twinkie, ABC are all the same meaning. As much as we will still hear the accent and some of the old ways. Those back in China will know she is different. Besides her accent, she will have more confidence but she will be less competitive. She will be more likely to small talk and laugh. And the next generation really will be every bit American as anyone from Europe or anywhere else.
The experience on an American school playground and the entertainment media here often put a defining mark on a child as American.