US citizen entering USA as non-citizen

The situation: Husband (UK citizen) and wife (US citizen) live together in the UK with their child, who was born in the UK and has never left that country. Child holds British passport. Per US law, the child is a US citizen (the mother meets the residence requirements outlined here and is automatically a citizen at birth) and is eligible for a US passport. However, the child's birth was never declared to the US authorities. From the point of view of the US, the child does not exist, and they do not know that the child is a citizen. The parents aren't interested in having the child be a US citizen or have a US passport, although technically the child is a US citizen.

The question: Can the child enter the US on a British passport (when travelling with both parents)?

My speculation: I know that US citizens must enter the US with their US passport (see e.g. here), but in this case, the child does not have a US passport and no-one knows that they are a citizen. So I suspect that the answer to my question is "no, it is a violation of the law for the child to enter the US on a British passport", but practically speaking, is this regulation enforced, especially for a child who (for all intents and purposes) does not exist?

EDIT: To be clear, I'm specifically asking about arriving in the US by air on a flight from the UK. Will the child be able to enter the US on their British passport, or will the border officials say "we suspect you are a US citizen" and levy a fine or some other punitive measure?

Best Answer

I'm answering this myself to summarize the discussion in comments, and because no-one else seems to have offered a clear answer.

Original question: Can the child enter the US on a British passport (when travelling with both parents)?

Yes, the child can enter the USA. There are two scenarios for this happening:

The child enters as a British citizen, without additional questioning at the border.
At the border, the parents are asked if the child is a US citizen, or are asked questions to ascertain the child's eligibility for a claim to citizenship. (That is, the mother's nationality and the residence history of the mother.) Once it is ascertained that the child is a US citizen, the parents are given a lecture that the child should be travelling on a US passport. Since the authorities are satisfied that the child is a US citizen, the child is free to enter the US. No fine is levied.

Under scenario 2 it's unclear whether the UK passport would be stamped, or if there are any consequences for the parents if they had (knowingly or unknowingly) made a false statement on the ESTA application.

Implicit question: Is this a good idea?

Probably not. Particularly in the long term, several commenters noted that US citizenship carries tax obligations, and by not recognizing one's citizenship, one could fall afoul of the tax obligations and unwittingly violate some law. The parents ought to get a US passport for their child