Immigrants get old and sick too and their children need schooling. What you are proposing is one giant Ponzi scheme.
What nobody ever mentions is the capital cost of providing all this new housing. Then there is all the necessary infrastructure to go with it - roads, electricity, gas, water supply, sewerage, it goes on and on. Somebody has to pay for all this and if it hasn't been brought into the country with the immigrants, as is the case with countries such as New Zealand, then these costs have to come out of the existing economy. Then some smart Alec will remind us of our commitments to reducing the amount of CO2 we produce.