There's also a phenomenon where migrants are more likely to cling to their prototypical tradition than people who stay.

For example, the Taiwanese use traditional Chinese whereas Mainland China use simplified Chinese. Or the orthodox Jewish communities in Brooklyn. The Vietnamese diaspora.

That's what they say in anthropology, and there is truth to it, but I think you could find better examples. Israel is a new country that was populated by immigrants by and large. Hasids sought others out and settled like places because they wanted that culture, on the other hand secular jews in nyc are indistinguishable from anyone else (and they too are immigrants). China adopted simplified logograms to combat illiteracy. Honk Kong was not an immigrant city and it retained traditional characters. Cities in Vietnam exhibit some cracks in traditional culture, but go to the provinces and it's still traditional.

> For example, the Taiwanese use traditional Chinese whereas Mainland China use simplified Chinese

It may be political though. As in Taiwan keeping up with the "true" Chinese tradition -- as opposed to post-Cultural-Revolution China.

Orthodox jews are not particularly representative of Jewish migrants. I suspect your premise in general is false.