alt Hacker News> we just have every person registered in a central database from birth
"Just" is doing a lot of work in that sentence!
A human female can have sex once and pop out a new human 9 months later regardless of her connection to any official social systems or state apparatus. She could disappear into the woods as a hermit and produce a completely uncounted unknown new person.
To the degree that that doesn't happen, it's because a country has spent generations building a giant high trust society with good widely available medical infrastructure and a culture where almost everyone believes it is better to use that than to go it alone. Building that system requires the powerless to organize themselves and counterbalance the powerful elite who otherwise have a tendency towards despotism and corruption. That in turn requires a lot of shared culture so that the powerless feel they are all one tribe and not fractured out-groups (a reality the elites are constantly incentivized to manufacture). You need good education, mobility, safety.
An easy census is the very pinnacle of a successful society and only in a few places in the recent past has any country reached it.
> it is better to use that than to go it alone.
frankly I don't think in any even half modern country you can go at it alone. I struggle to imagine how someone would physically manage to evade public authorities here in Germany where schooling is mandatory and any kid not in the education system would sooner or later be caught. There's barely even a place so remote authorities or other citizens would notice you and report you. You couldn't go to the doctor or anywhere really without identification or insurance.
So I think it's less of a function of trust and more simply of modernity, you're not going to escape attention for too long unless you're a trained spy or something