Many immigrants come with children.

I wasn't complaining about the inclusion of those children. I was complaining of the inclusion of children of immigrants born in the US which constitutionally makes them American citizens.

Law enforcement costs money and pulled away from normal operation.

Which is a choice we make. It is not inherent to immigration. For half the existence of this country we spent zero on regulating immigration.

if migrants didn't generate net revenues positively in their country of origin, what makes you think they generate a net positive in the new host country?

Failure of productivity results from a corrupt and inefficient government in places like Venezuela. It has little to do with the capability of people. Go to any construction site or kitchen in the US and you will find them staffed with mostly immigrants. Labor created value and anyone can do labor if managed effectively.

Furthermore, why do municipalities like NYC have to cut services? Why do they have to evict migrants from shelters?

Because they don't have sufficient funds to do so which could easily be fixed if xenophobes in government didn't block taking action.

Using their logic, we should take in all the people in poverty in the world, and boost the GDP to astronomical levels by funding all of it.

Correct. Labor is the most valuable natural resource on Earth.