Totally agreed, Aadhar is not proof of citizenship, its same as SIN or SSN. But when issuing Aadhar for a new born with an Indian Birth Certificate the legal status of the baby will be marked as citizen of India. Aadhar cant be issued without a legal status. This has caused trouble when applying for visa or oci in several cases.
For instance: Typically prior to OCI, the Indian passport is surrendered first there by renouncing Indian citizenship, that deactivates Aadhar as well. If required new Aadhar can be requested as a foreign national.