Switzerland is a diverse society with lots of immigration and it is also a high-trust society
Denmark is still a fairly high-trust society, not to the level of Switzerland or Japan. We're seeing certain items in supermarkets being locked away or chipped to prevent theft. Now that's not just because of immigrants, Danes steal from the supermarket as well, because prices on many items are increasing rapidly.
If it adds enough of illegal immigrattion or low-grade legal one, it wont be a high trust society anymore.
There are countries that are equal or much smaller than Switzerland with 10x worse crime and low trust. Just look at Jamaica.
And there are countries 12x bigger than Switzerland (like Japan) with high trust and low crime.
LA "the city" might be less but you can't tell where LA ends and it's other parts begin. It's one giant metropolis. Same with NYC.