Anchor babies are in the US illegally—Just like their parents.
Anchor babies are stakes set in the ground for a claim - nothing more.
The claim, like a gold mining claim, is not valid until it has been properly registered in the local repository of records for this very purpose.
There was an old expression, from days of the California Gold Rush, of “claim jumpers”, those who illegally moved the stakes to encroach on the claim of another, before a formal registration of the claim could be made.
The claim still has to be validated by the proper authority.
When the child is of the age of majority, a special application to either pursue the citizenship of the parents, or the accident of geography, should be made, without this “dual citizenship” practice. But that applies to the child only, not extended to members of the family, who would have to go through the whole process of applying for legal residence and getting on the pathway to citizenship by the means already stated in existing law.