[seabass-labrax]

It's interesting indeed, but is missing an important factor. Every niche requires resources for someone to fill it: time, at a minimum, but also raw materials (engineering, art), land (agriculture, wildlife preservation), power (pretty much everything) and so on. These are all finite, although some are now used more efficiently than they could have been in the past.

By having more children, you contribute to more people fulfilling their purposes in the future, but this is true only to the point where resources would become too scarce when divided between the niches.

I would guess that in the future, the Earth could sustain maybe double its current population, due to much more efficient resource utilisation and extraction, relieving the demand on these resources, and the large number of people who would prefer to live in cities, reducing the demand on land. But the Earth could not sustain such a growth of its population immediately; we need time to let society and technology improve and adapt.