The analogy of the house does not fit very well (countries do not invite foreigners, they simply accept or reject their entry), it seems to me better to take it as a "party", at a party you are going to accept well-behaved guests and you are going to to turn away guests who misbehave.
The guest will pay the same taxes as the citizens, so the house is also paid by him.
Again, I did not find any arguments from the philosophy behind the current migration system