I guess something like that will be inevitable. Unfortunately it will have to be combined with a control of population size or it will be unsustainable.
Population will continue to stabilize and possibly fall in the developed world and population growth will lessen in the developing world.
Also, a life on basic income would probably be similar psychologically to unemployment -- more depression, disease, shorter lifespans, etc. These things contribute to a reduced rate of childbirth.
It would be difficult to let kids live in squalor, though. Presumably parents would receive at least some extra money, but perhaps it would decline with the number of children.