Michael,
You're partially right, but the plain truth is that not only has Europe failed to assimilate immigrants on a economic level, but they have also failed on a cultural level despite their well-intentioned, feel-good rhetoric. The whole "multi-cultural" model merely creates a society of large groups of individuals who have no connection to each other. In France, which has failed far worse than most European nations, the Socialist Welfare state combined with "respect" for diversity creates a short term "good feeling" among the dominant class, but it has proven a prescription for long term disaster.
Correct. Thankfully, America has not been taken over by that attitude, and not coincidentally we have the world's most peaceful Muslims.
It should also be said that America's nature (based on ideas) makes it easier to assimilate people than Europe's nature (based on geography and history). Any idiot can become American, just learn English, eat a hot dog, go to a baseball game, and learn to like cowboy movies. You have to be born French, or German, or Italian because European identity is historically rooted in ethnic identity much more than identity in America.