You probably should consider applying for a certificate of citizenship as backup. It is not needed for your child to obtain citizenship, it is just proof. However, the cheaper, easier and faster proof of citizenship is the passport. However, the certificate might be useful to avoid some hassles from agencies that don't understand that there is a class of citizens who derive naturalization through their parents and don't have US birth certificates or any other proof of citizenship, except the passport. Some agencies expect to see a certificate of naturalization or of citizenship.
By the way, it seems that Canada requests children born abroad that are looking to obtain a passport to obtain a certificate of citizenship first. Perhaps the US will end up doing something similar. I hope not. I think we already have more than enough bureaucracy.