Nope. This is a hobby horse of mine that I’ve read up on extensively. From the very beginning of the industrial revolution it’s been true that women in third or later generation middle class and up households have had under 2.5 children born to them over their lifetimes. Today that figure is about 1.6. Rural folks, immigrants and their kids still tended to have bigger families, which boosted the overall numbers, but the science of demography has pretty conclusively shown that urban living tends toward long term native no growth outcomes, even before the advent of modern contraception.
Reasons vary, but include the fact that urban living flips the economic situation from one in which kids are an economic help to one in which kids are an economic burden, so urban women tend to WANT fewer kids. What women want has been shown to be THE largest determinant in how many they actually have. Also urban life tends towards later marriage due to education and training requirements, which tends to eat up much of the most fertile time and increases the incidence of infertility (can’t have kids at all). But also, it turns out that humans are mammals and mammals ALL produce readily discernible symptoms of fertility. It’s not like NFP is rocket science. At minimum, you need toilet paper and the ability to count to three to practice it. Earlier societies just did so informally rather than pretending that it’s a complex issue that only trained medical staff can instruct you in.
And, for the record, “natural” doesn’t mean forests, bugs and bunnies. It means “according to one’s nature.” The velocity at which I travel from point A to B doesn’t affect my nature as a person. But intentionally sterilizing my wife (or myself) so that I can have sex with her without a baby resulting DOES affect my nature as a person. It changes what that encounter IS.