Net cost to a national government and GDP per capita are not the same thing. Presumably these people become more productive by moving to more developed countries; that's the general reason that people immigrate to particular places. My impression without looking at the data is that US GDP per capita has continued to increase despite large (called a crisis by Republicans) numbers of immigrants during the Biden Administration. And given that these people are not citizens of the US, presumably they will not be eligible for all benefits granted to citizens which would decrease their cost to the government.