1000 planets isn't really enough for all of humanity.
Of those 1000, there maybe 10 Earth likes capable of sustaining human life at the same capacity as Terra.
The rest may require terraforming, terrestrial bases with limited capacity, orbital bases if the surface is inhospitable, etc
There's 7 billion currently on Earth, that number isn't rising faster due to some countries imposing population control, others the death rate is as high as the birth rate.
How quickly will the population explode once we reach a post scarcity society?