Birth rates are declining throughout the industrialized world irrespective of population density. They are very low in dense cities, but they're also low in small towns and villages.
If you give a woman something more interesting to do in her twenties than give birth, well, she's probably going to. Nobody's figured out how to industrialize and not decide that women are better off in the office than the kitchen. Currently, being 23 is such an overload of stimulus that for both men and women, a baby would be a massive setback.
It appears to be inevitable, as the social and moral changes necessary for industrialization lead to devaluing home and family life. In an industrial society, a "good man" isn't one with four kids that have been raised reasonably well, it's a man who has burned the midnight oil building out his startup and flipping it for $100m by the time he's thirty-five years old.
And if that's what a good man is, what is a good woman? Well...uh...I guess it's one who stays in school, preferably until she's 25, and devotes her youth to the service of her employer and the creation of GDP.