This is a good observation. One possibility is that globalism serves as a vector for communicating certain cultural habits. A natural place to look is the US as it has been the primary globalizing force in recent history. American popular culture (TV, cinema), NGOs, the influence of American universities, etc. all serve to spread ideas sell a certain vision of life. It doesn't matter if the ideas are good. These methods appeal to the emotions.

And this is not a bad suspicion, as it seems that the inverse relation between number of children and wealth, when people are otherwise permitted to have children as they wish, seems to be characteristic of consumerist societies.

Parenthood is very central to our humanity. Fatherhood is a core expression of masculinity while motherhood is a core expression of femininity. Of course, parenthood isn't always expressed by having biological children. In the Catholic Church, for example, priests assume a paternal role in their parishes, while religious sisters often assume a maternal role by becoming teachers or by mentoring young novices. In such cases, such people choose to sacrifice their biological parenthood for the sake of a worthy good, and here, a parental role that isn't biological. Pathological expressions of the subconscious parental desire can be seen when people treat their pets like children (like those women who push their dogs around in strollers and pamper them in obscene ways).

However, in a healthy society, most people will choose to have biological children. The outliers do not disprove the general. And the fact that so many people are actively choosing not to have children is a sign of cultural decadence and decline.

When you speak of "autonomy", what is this "experience" of the one life you have in mind? Being a parent is, of course, such an experience, and not just one of many you can choose from, but an experience that is deeply central to being human. That so many are choosing not to have children is not the result of some spiritual awakening where they are choosing to sacrifice having children for some worthy noble end. The argument from autonomy is really an argument from self-indulgence. The objective richness and centrality of parenthood to human life is typically traded by such people for a life of pointless and empty "experiences", or lesser goods. By hiding behind "autonomy" and some relativized notion of preference, parenthood becomes as banal as choosing a flavor of ice cream, which it isn't.

No one is forced to have children, and no one in particular needs to have them, but as I said earlier, when a culture is healthy, most people will choose to have them. That so many are choosing not to is not a matter of choosing chocolate over vanilla, but usually, it is a matter of trivializing one's life by choosing comfort, self-indulgence, and the avoidance of responsibility and commitment. These stand in the way of a voracious, egotistical autonomy. But such autonomy does not make us grow as human beings. It stifles our development, feeds narcissism, and imagines us and our appetites as the center of the universe. In the end, it is a dehumanizing recipe for unhappiness and misery. So the basic problem is not firstly the falling statistic, but the narcissistic attitude engendered by vacuous hyperindividualism.