Depends what do you mean with adopted. A children adopted due to abandonment or loss of parents will still have the original parents in the certificate.

If you mean adopted at birth after the practice or similars, their birth certificate is invalid as you have read. In this case a child not having a valid birth certificate means having an invalid Italian citizenship meaning a legal risk for the parents and unability for legal access for institutions and documents, like creating a passport. This is a massive problem as a partner in surrogacy might be unreachable as done illegally, and they would need to sign the new birth certificate and state that child as their own. It also means only the registered member of the actual couple will show as a parent, and there are a lot of context where both registered parents are needed for signing.

Recap:

• Invalid documents, until the donator shows up
• The donator must become present in the child's life due to multiple documents needing signing from both registered parents
• Only one member of the actual couple will be able to present themself as parent. It would make it illegal for the non-registered person to even pick up their child from school unless a extra permit is written.

Surrogacy has been banned in Italy in 2003 with a claim it promoted child-trafficking and prostitution. Currently, the law is defended by many right-wing parties (extremely powerful in Italy) claiming living without a biological mother or father is a violation of human rights for the child. At the moment, surrogacy is punished via a nasty fine (up to €1m) or jail time up to 2 years. The current government wants to expand this punishment also to Italian couple that had this practice outside of Italian soil. On a side note, same-sex marriage is also banned in Italy.