Oh, wow. Literally your neighbours reporting you to the authorities and the authorities have enough manpower to come knocking your door down. Literally your fellow family members reporting you to the authorities when you didn't turn up for Mass. All 100M of you.
I wonder who feeds, clothes and otherwise sustains this massive standing army of informants, clerics, soldiers and whatnot...
Scarcity, my ass.
Given how the population of the
entire world in the year 1 AD is estimated to have been around 150 million to 300 million, a single country won't have 100 million thousands of years before that.
Some pages ago
Reinhardt pointed out that adventurers should be allowed only to do official missions from the church. You've replied that he could ask the same question about other fantasy settings. My point is that this criticism can't be applied to other settings because social control in these is not robust enough to make something like that feasible. On the other hand in your setting where every single pregnancy is tracked by the central government, it's easily doable.
Having bureaucracy doesn't mean you can physically control people every day of their lives, or have the desire to do so. They just control the population due to the many problems that would arise if there is overpopulation. And why would churches want to send them only on official missions? Adventuring is their job basically, and small groups go for either personal riches or helping local problems, not business which the churches occupy themselves with.