Why is this so? Well, this strategy essentially produces a limited pool of offspring, all with huge amounts of per capita resources in both human and economic capital. It makes them socioeconomically very competitive. The downside is that the species as a whole becomes less biologically competitive.
But this is not a new problem. Humans have been using technology to avoid the problems of simple biological competition for ages. We can compete with large predators (in fact, we've eliminated many of them or reduced them to zoological exhibits) by using weapons that vastly increase our sensory and attack range. We can compete with the environment by using engineering of all kinds. And we can mobilise energy quantitatively more effectively (although not more efficiently) than most other species. A smart human with high resource levels will out-compete a less-smart, less-resourced human — which is why you see dropping birthrates once a society gets freer access to technology.
In a city-state, where there are few natural threats, the main threat is socioeconomic, no matter what people moan and groan about. It thus makes perfect sense to see a drop in fertility levels in the vast majority of cities and city-states unless they have a large hinterland that is not urbanised.
However, there is always a bump in the implementation of such a strategy. This normally comes in the form of people moaning and groaning about low fertility as if they lived in an agricultural, low population density, high resource density environment. Ridiculous. We're not bacteria in a particularly rich chicken broth.