"and it's not that there is no burden on the immigrants. they still have to learn to understand the local language, culture, rule of law, etc..."

And there is the problem. You see, in modern Sweden (and many other European countries) it's entirely possible for migrants to live for decades without learning the language, understanding the culture, or even respecting the rule of law.

The majority needs to welcome and support the minority AND the minority needs to do their best to integrate. Right now the latter part is badly failing in Sweden, which is the reason for extreme amount of gang violence and social inequality plaguing Sweden. It's not even fault of the Swedes or the migrants, it's a systemic problem. The migration and integration policy is broken.