Customs? Yes, hold on to those. Languages? Never. That has NEVER been the case. Initially, each of the ethnicities held on to their communities, but the idea throughout was that NOW YOU ARE IN AMERICA. Be an American.
Speak the language.
It has never been the case that these immigrant communities stubbornly stuck to their languages rather than adopt English as their new language, and it was NEVER the case that children be encouraged to do the same.
On the contrary, the more distance immigrants could put between the old ways and the new, the better.
Languages YES. I already gave you an example of a group that kept their language it turned into a dialect. And there’s plenty of other example, if you’re in a major city you’ll have these ethnic conclaves (Chinatowns, Little Italies, whatever groups you have), and there will be groups of people there speaking the old language, signage will be in the old language, sure most of them will also be able to function in English but the old language will be present. So obviously it hasn’t never been case, and you are simply wrong.
Have you been to Chinatown in any major city? Chinese signs all over the place. That's not a new trend either, and it's not limited to Chinatowns. As late as the late 1800s, for example, New York's third-largest newspaper was a German language paper.
Also, even where immigrant communities have assimilated quickly, "quickly" is a relative term. First-generation immigrants (historically and today) typically continue to speak the native tongue, while picking up a bit of English - largely because it can be very, very difficult to learn a new language as an adult. Second-generation immigrants have historically assimilated a bit more, primarily speaking English in public, but the native tongue at home. Finally, by the third generation, immigrants typically speak English almost exclusively, while picking up a little bit of the native tongue.