Declining birth rate is not a problem that requires fixing, it is a mercifully wise collective decision by intelligent creatures who've become educated and aware enough of their place in the biosphere to recognize the destructive effects of their own overpopulation. The idea that declining birth rate is decidedly NOT economic - lower birth rate does not arise among the poor and uneducated in the world.
There is no problem in today's world that would be mitigated by increasing birth rate. I live in a region where there is a burgeoning elderly population and sometimes people say - we need more young people in this economy! But that does not mean that having more babies here is any help: by the time they are adults, the wave of excess elderly people will be gone. Economic crises are far more immediate than generational solutions - if a region lacks workers, economic forces are more effective to relocate workers than biologically growing new ones. Of course, governments often fail to anticipate needs and adjust migration policies in a timely way, or housing policies, or other such issues that create barriers contrary to the economic forces.
What the author is saying, I think, is that the inevitability of the tragedy is the right-wing concept. The concept of the commons is totally legit and the tragedy that can befall it from unregulated use is also clear. The right-wing concept that is dubious is that humans will self-regulate and do not benefit from governance.