I guess the issue is not immigration per se, but the method. These conversations often seem to assume that the worst cases are the most common. In the past, there were a lot of Italian migrants. Although now accepted by most Australians, there were certainly a minority involved in organised crime. My son's partner is a migrant from China (to NZ). She is a highly paid (and taxed) contributor to society. The term immigrant is rather broad. My doctor and my dentist are immigrants.
For the last 30 years of my working life, I mainly worked as a music teacher in private music studios. The number of my colleagues born overseas was quite large. These people were the best and brightest. Here is a picture from when I retired. There are Irish, Vietnamese, Chinese, Hong Kong, South American, South African, British, and probably more. These people were all smart and talented, and I loved working with them.
I am also an immigrant. My family arrived in Australia in 1964 as "ten-pound tourists" We lived in a new city called Elizabeth, which was full of immigrants, mainly British but other nationalities as well. A few immigrants failed to adjust, and there was crime associated with this. I don't have the figures, but I doubt it would have been much greater than from Australian-born people.