The government is greedy AND retarded but also EXTREMELY short-sighted.
Awful, low IQ migrants are a better short-term investment than taking care of your current population; they are guaranteed votes since they are welfare recipients, they drive the housing market down, you can accomodate plenty of them in small places, you can hire multiple of them before you ever have to pay the same amount you'd pay a local for their work, they are low maintenance too, their spending habits are garbage too (which is good for the government), in short, they are as short-sighted, greedy and gullible as the people who let them in, just more retarded than them, somehow.
But these are just short-term benefits, what do you do after you essentially kill the part of your population that pays your taxes/your salary? What do you do down the line when you are outnumbered by the bands of migrants you let in? What do you do if they start getting into politics and they start voting for their own instead of you? What do you do when the number of gibs becomes unsustainable?
The answers to these questions is that they simply have not thought far ahead and they probably don't care either. The government is mostly old fucks, they'll be senile or dead by the time they are out of office. Their pockets will be full and they'll not need to give a fuck either, it's a problem for the next round of idiots to solve. They are essentially trading "tomorrow" for "today".