I don't know about Korea but if memorizing an ID number works, then that's just a badly designed system.
I'm not sure what your argument is really, unless you're saying there's technically and absolutely no feasible way to securely verify the age of a person before allowing them to access an online service (even if you allow the government to be authoritarian)
the actual users of each simcard did not have to identify themselves. so at least then it wasn't about age controls, but it obviously would allow tracing the owner eventually.