Well, you raise some good points. I can only look to history for my explanation: the great waves of immigration saw Poles, Italians, Germans, Greeks and many others assimilated in large part by learning English in the first generation and then forgetting their ethnic language starting with the second.
What else could be characterized as a homogeneous identity within the USA? Ethnicity is out. Race, clearly not. Obviously, not everyone is wealthy. Until the recent wave of Spanish-speaking immigrants and Spanish only areas within the country, English was the one great uniter. Alarmist? Perhaps, but the US has never faced a long-term threat to its collective identity such as this.
So I would be willing to lean on businesses to foot the bill for aggressive English-teaching and legalization paths for illegals they employ. We all know the businesses reap the great benefits from mass immigration anyway.
Before I veer too dangerously into leftist terrain, let me also say that we need to declare an official language this instant, and build a much better border wall.
How would I pay for all this? Cut defense spending, of course. I don't see the US as economically able to project global power for much longer. Make aggressive steps towards improving relations with the Middle East at the expense of Israel in the short term towards cutting costs rapidly--and avoiding any more Mid East conflicts. In the long term, court Russia+India as opposed to China. The US will not easily be able to afford another Cold War; however, I believe China will be contained in the years to come by a US-Russia-India alliance.