I think first off unsustainability is a minor concern. At a birth rate of 1.7 we'll still have more humans in 2150 on the globe than we had in 1980, so that doesn't sound so alarming.
More importantly I think the author points to a real problem but finds the wrong solution. It's indeed true that family is a form of social support, but it's not the only one. The author laments the breakdown of the nuclear family but it is the nuclear family itself that was probably one of the worst inventions we ever made.
Instead of trying to rebuild the socially impoverished nuclear family, the low birthrate can be used to rebuild community. Socialisation not out of any tribal obligation, but voluntarily. Creating institutions in which people cooperate and live together rather than small suburban homes full of lonely grandparents.
