Japan offers child allowances, free schooling and parental leave. If money was the only problem, the birth rate should be recovering not declining.
It's the same in other countries with strong welfare support, it's more of a cultural shift if anything. People are marrying later and are more career driven, by choice, they are not forced.
Even if housing was cheap and childcare was free, not everyone would want to sit at home and look after 4 kids. People want careers, hobbies, travel, etc. Blaming low birth rates on the state is just a convenient cop out when the reality is, people's