Funny, I've lived overseas as an international schoolteacher for most of my adult life, working with the wealthy, privileged children of 'crazy, rich Asians,' so a lot of those stereotypes feel quite remote to me. Thinking of any of my students as "submissive Asians" is definitely amusing. In my circles, they're definitely informed by Hollywood, not by experience with military or EFL teachers. Though I suppose the situation you depict is still more widespread.
I think you're correct. The common Western stereotypes of Asian women are largely wrong today, however much or little truth there may have been to them in the past. (Not trying to single out women here, just that it's the subject under discussion. Stereotypes of Asian men may be even farther from the facts.)
That could be said about most stereotypes of **ANY** group. By definition, a stereotype takes a group of people and says a common characteristic applies to all of them merely because it applies to some of them, or the person talking thinks it applies to some of them. Now of course stereotypes have to have SOME basis in reality, or they wouldn't ever have become widely believed. But since we're talking about Asians, today's common stereotype of Asians as very smart and highly educated is the near-exact opposite of the stereotype of Asians in the 1800s, who were regarded as dirty, uneducated, "inscrutable Orientals" who were prone to criminality and vice. The term "Chinatown" today has a completely different connotation than the term in movies of just a generation or two ago.
I think what's going on here is that you are -- your words -- "working with the wealthy, privileged children of 'crazy, rich Asians.'" (Yes, I caught the movie allusion.)
That is a very different category from most of the women who American soldiers were encountering in Japan of the 1940s and 1950s, Korea of the 1950s and 1960s, and Vietnam of the 1960s and 1970s. It was a small subset of the Japanese, Korean and Vietnamese population who had a reason for extended contact with Americans during those eras, and while Japan entered the modern world economy by the 1960s and Korea did so by the 1980s, both countries continued to have serious internal economic problems for a very long time which to some extent still exist. The "Asian Tigers" are not all furry and nice, and there are serious income disparities, even today, that led to social problems that caused some women to seek out American men, and seeking employment on or near American military bases was one way to do so.
While the majority of the American population, even at the height of wartime, never wore the uniform and many of those who did were not deployed to Asia -- even during and following the "shooting wars" in Korea and Vietnam, the Cold War required a HUGE military footprint in Europe and smaller numbers elsewhere -- American military personnel who came back from Asia related their experiences or their beliefs about Asians and that created a perception of Asians in the broader population of the United States that never applied to more than a small portion of Asians. That portion was disproportionately poor and seeking opportunities that could be found by contact with Americans.
Today, the wealthier an Asian is, the more likely he (or she) is to travel overseas, to work overseas, to study overseas, or to want to learn English while staying in his or her own country. An Asian woman today who is willing to marry a Western man is likely to have met him in a professional context in business, or while studying together in school. That means she may very well be a highly educated woman who, at least by the standards of her country, is quite "progressive" or even "liberal," and there's a good chance she's going to oppose her parents' objections to an American son-in-law.
Before someone accuses me of stereotyping "poor vulnerable Asians who were seeking out American soldiers because of neo-colonial military expeditionism," there's an entire song written in the 1950s by an Italian band leader, "Tu Vuo Fa' L'Americano," commonly translated as "The American," ridiculing and mocking Italians who cozied up to American soldiers during the American occupation of Italy. That song continues to be sung today in Europe because there are a lot of people in countries all over Western Europe who love to say bad things about Americans and mock people who like Americans, forgetting that it was largely the United States and Britain that saved Europe from Hitler and Mussolini.
Here's a video of the original Renato Carosone song, L'Americano, from the 1950s:
Here's a "cover" by a Hungarian group that really ought to be a lot more grateful to Americans given Hungarian history:
And here's a modern "cover" of the same song, performed by an Italian band that performs in southern France for French tourists who have their own reasons for mocking Americans:
Here's a (rough) translation into English of the Italian lyrics, not all of which are in these videos and some of which have been changed in the modern performance by Italians for a French audience.
You're wearing trousers with a tag on the back
and a cap with the visor turned up,
parading around Toleto
like a dandy trying to show off
You're acting all american,american, american,
listen here: who's asking you to?
You want to be all trendy,
but if you drink "whisky and soda"
you always end up sick!
You're dancing rock and roll,
and playing baseball,
but where'd you get the money
for the Camel cigarettes?
Mummy's handbag!
You're acting all american, american, american,
but you're born in Italy, listen here:
there's nothing you can do,
ok napoletano?!
You're acting all american, american, american,
How can your loved one understand
if you're speaking half american?
When you're out loving under the moon,
where do you get a phrase like "I love you"?
You're acting all american, american, american,
but you're born in Italy, listen here:
there's nothing you can do,
ok napoletano?!
You're acting all american,american, american...
whisky soda, rock and roll.
The song "Tu Vuo Fa' L'Americano" has nothing to do with race. It was originally written by white Italians mocking white Americans and is now popular among white liberal Europeans who mock white Americans who are viewed as foolish backwards and uncultured "rubes."
It has everything to do with a very proud people who fought and lost a war, and were mad when the winners sent soldiers who brought their culture with them and caused people to want to be like the victorious Americans. Sorry, guys -- you lose a war, there are going to be consequences. Losing a war to Americans is a lot less bad than losing wars to a lot of other people. Renato Carosone would be dead or in a Siberian prison camp if he had lived in East Germany and tried writing a song like that about the Russians in the 1950s.
Furthermore, I find it interesting that some of the Italian singers in the third video have blonde hair -- positive proof they are descendants of some of the "barbarians" who fought and defeated the Italian troops of the Roman Empire fifteen centuries ago. A jazz singer doesn't really matter, but some of the most ethno-nationalist figures of modern Europe have ancestries quite different from their current nationalist rhetoric. That's fine in America which has been a nation of immigrants for centuries. It's not fine for people in Europe who advocate a "blood and soil" ethno-state.
I don't know very many liberal Europeans who will argue that Europe would have been better if America had lost the war that prompted Renato Carosone's song. Now granted, Mussolini wasn't Hitler, and a case can be made that history would have been quite different, and quite a bit better for Italy, if Mussolini had followed Franco's model of avoiding a military alliance with Hitler. But Mussolini was "bad news." He needed to be defeated, and Americans deserve the credit for doing so.
The people who blame America for stereotyping Asian women based on their contact with Japanese, Korean, Vietnamese and Filipina "war brides" ought to remember that lots of American soldiers met, had relationships with, and sometimes married Italian and German women, too.