Interesting that you shoe-horned economics into a discussion about culture and crime.
But anyways, I think Japan, and China would disagree with your arguments.
But more importantly, I think it is the political and social realm where "diversity" causes the most friction.
Increasingly, much of our political, social, and cultural debates and discussions are focused on diversity and racial issues.
The more "diverse" one's citizenry, the more they will be saddled with these kinds of hot-button issues. The more identity groups, the more separate political constituencies will exist.
They crowd out, or influence, almost all other discussions around politics and economic. Increasingly social-justice/multiculturalism/diversity is involved with every issue in the political sphere. This is not a positive development.
To the degree these kinds of changes happen slowly, the more diverse cultures assimilate to the host culture. Diversity supporters do not generally support limited, slow immigration, but rather open borders.