So you would think, but although South Korea (for example) has a similar low birth rate, their baby boxes gets plenty of traffic, unfortunately.

People who have the largest barriers to contraception, abortion care, sexual health care and education are the the ones most likely to have their children end up in baby boxes.

There's a doco on youtube called Babybox : S. Korea's Paradox of Low Birth Rate that's well worth the watch (though brace yourself if you're a crier, it's rough).