Can there be an express provision in the marriage law that children's household registration follows their parents?

Regulations of People's Republic of China (PRC) Municipality on Household Registration

Within one month after the birth of a newborn baby whose parents are residents of this Municipality, the parents or guardians of the baby shall report the birth registration to the local police station where the baby's father or mother has a permanent residence by presenting the birth medical certificate, the supplementary page of the birth medical certificate, the marriage certificate and the baby's parents' household registration book (if they report their birth with the father, they must bring their mother's household registration book and ID card). Women from other provinces and cities are married to residents with permanent residence in this city, and babies born after August 7, 2003 can declare and register their permanent residence at the household registration authority where their father's permanent residence is located. Such accounts are examined by the public security police station that handles birth registration.

The certification materials to be reviewed are as follows: (1) the marriage certificate of the baby's parents; (2) the baby's "birth medical certificate"; (3) parents' household registration book and ID card. Babies born out of wedlock with their father or mother declare their birth registration in this city, which is accepted by the police station and approved by the public security bureau (county). The certification materials to be reviewed are as follows: (1) A written application from the applicant's father or mother asking the baby to declare permanent residence in this city; (2) the baby's "birth medical certificate"; (3) provide prenatal hospital examination certificate with the mother applying for permanent residence, and provide paternity test certificate with the father applying for permanent residence; (4) parents' household registration book and ID card.