I agree that it isn’t possible currently, but I don’t think it needs to remain impossible in a not-too-distant future. Assuming 1) a proliferation of surveillance technology, 2) increasing formalization of individual identity, continuing the trend from single names to social security numbers to RealID etc., and 3) ubiquitous gene sequencing – all of which are on a steadily upward trend – the policy could be enforced through some substantial penalty, and monitored through AI empowered surveillance that notices pregnancy, or recognizes new faces and then determining parentage from genetic sequencing.
Note also that China’s one-child policy is not too far from this in terms of what’s necessary to enforce it. My impression is that that policy has been mostly enforceable, particularly in cities, as reflected in e.g. the substantial shift in gender makeup of China following its implementation. That isn’t global of course, but China is enormous and populous. A strong global government shouldn’t have too much more trouble.
Another way to think about this problem is to change the ‘globe’ we’re talking about. While enforcement could be insurmountable over all of Earth, it would be a smaller lift in the context of a space station, Mars colony, or generation ship. And controlling birth might make sense in those contexts, where resources are scarce and a just distribution of a scarce right to reproduce is necessary. However, those economies are unlikely to be market economies, because market economies are a bad fit for small groups, particularly where individual actions can have such a high impact on everyone’s lives.
I forgot to mention in the OP why the specifics of how it’s implemented could be relevant. Suppose the policy is enforced under penalty of death for the parents. Would some people choose to have a child in spite of that? Many people are willing to die for their children, so it’s not impossible that people would choose to die to procreate. It may not be possible to have a penalty high enough to deter ‘off-market’ births.
If the policy were enforced by detecting and terminating unlawful pregnancies, then additional penalties would be sufficient to deter that kind of rational lawbreaking: there would be a cost to those breaking the law with nothing to show for it.