Governments that take in many immigrants also see benefits from allowing them to keep their old passports. Research suggests that immigrants who do not fear losing their existing nationality are more likely to pursue naturalisation in their adopted countries—and subsequently more likely to integrate than those who maintain long-term residence as aliens. (Whether they go on to make better or worse citizens is harder to prove.)
In this context, what is the benefits?
CAUTION: NOT A TEACHER
I feel that "benefits" refers to:
(a) The fact that they are "more likely to pursue naturalization."
(b) The fact that they are "more likely to integrate."
(a) More eager to learn the native language.
(b) More eager to "become one of us."
(i) For example, some immigrants who come to the United States sometimes put
stickers (signs) on their car bumpers that say "I love [name of their native country]."
This really irritates many Americans. According to your paragraph, letting them keep
their old passports might cut down on such feelings on their part.