It meant something to the industrialists, once upon a time.
The Ford English School, which Henry Ford ran to teach his employees English (did you know that you could only get the vaunted "$5/day" wage if you either spoke English already or took lessons, and if your home was inspected to make sure you were living according to American cultural values?), started its first day with learning the words "I am a good American." At the end of the class, for graduation, everyone got into a literal giant "melting pot" and waved flags from inside it to celebrate.
Ford's techniques were seen as so good at assimilating immigrants that if you went through those classes, it counted as your naturalization paperwork and you could become a US citizen. It involved a lot of hard work and being open to Ford's social workers saying "you shouldn't have livestock in your house, in America we do things differently," but for a long time, it really did work.
Assimilation is good because it can take the rough edges off. We started being ashamed of the idea of American culture, and once people felt ashamed to be American or act American, it felt even more shameful to try to teach people from other, obviously superior cultures to act more American.