If the child applies for a US passport whether as a minor or adult, he/she will lose the ability to retain an Indian passport, and further, will cease to be a citizen of India by descent if within six months of attaining full age the child does not renounce the citizenship of the United States.
https://ilw.com/articles/2004,1217-mehta.shtm#:~:text=If%20the%20child%20applies%20for,citizenship%20of%20the%20United%20States.
Your statement is incorrect.
If the child opts for the US passport, he/she will need to apply for Overseas Citizenship pursuant to the Citizenship Act of 2003, which was passed by the Indian Parliament on December 22, 2003, to grant dual citizenship (a.k.a. Overseas Citizenship) to persons of Indian origin who are citizens of certain countries. The legislation will also grant Overseas Citizenship to Indian citizens who may take up the citizenship of these countries in the future. At present, this benefit is being extended to persons of Indian origin of the following 16 specified countries: Australia, Canada, Finland, France, Greece, Ireland, Israel, Italy, Netherlands, New Zealand, Portugal, Republic of Cyprus, Sweden, Switzerland, United Kingdom and the United States of America.
Good point, however, despite the name, I don’t think you can legitimately call their “Overseas Citizenship” an actual citizenship in the usual sense. Holders of this status cannot vote, hold public office (or even employment) and cannot be issued an Indian passport. It’s sort of like a special status that allows them to go back to India easily, but with a pretty name.