The trend is universal because birth control is becoming universal. The only places that still have high birth rates are places where birth control isn't easily available (and religious cultures). It could be driven by other factors as well, but I'm betting it's mostly just birth control. We don't have a very strong innate desire to have kids, it is the desire for sex that human reproduction has mostly relied on. We're only a couple of generations into birth control, so we're only now starting to feel the effect.
I think you’d lose that bet. Women die in childbirth regularly. And it’s not birth control but our stratospheric advances against infant mortality that most strongly influence population dynamics.
