Apart from the many studies that show a "net economic cost" to American citizens, there is common sense. It is hard to imagine that the mass immigration that America has been experiencing is economically beneficial. How can millions of poor, unskilled,  unassimilated immigrants produce a positive economic result. It makes no sense. 

You stated that immigrants are less likely to commit crimes than native born Americans. Assuming that this is true, I am sure it gives little consolation to those who have been the victims of crimes perpetrated by immigrants. If your dead your dead, whether your death was caused by someone who was "less likely" to kill you or someone who was more likely to kill you. 

The Catholic church has never taught that any country should adopt the lawlessness and general patterns of how America has been treating aliens over the last 30 years. For example, read what Aquinas says about immigration.