> I don't think it's reasonable to "demand" integration

Yes, it is reasonable to demand people who come into a country adapt to rules - written and to a certain extent also the unwritten, of which Sweden has many - of that country. When in Rome, act as the Romans. This adaptation will never be 100% but that is not the point, what is most important is that newcomers learn to assimilate to such a level that the natives are open and willing to maybe integrate some parts of the newcomer's culture.

People who 'are the last representatives of [their] culture' can write a book about it while becoming part of their new culture since it is clear that their old one did not stand the test of time. They're much better off that way instead of living like cultural fossils for the likes of NPR and PBS to make documentaries about. By all means document what that extinct culture had to offer but life is for the living and culture is the commonly agreed upon set of rules how to live it.

Multiculturalism is a pipe dream, something dreamt up by people who listened to one too many version of John Lennon's Imagine. It has been shown not to work time and time again, it makes it harder for people coming in to a new country to assimilate and integrate because there is no clear target to aim for. Culture is not a fixed thing, it evolves through time by adopting new things and getting rid of old customs. Multiculturalism does not call for cultural evolution, it calls for revolution: here's a whole new culture, now deal with it. Revolution hardly every works and when it does it tends to go badly for those on the wrong side of it.