In this case it's clear that the children were not literally deported. The parents were given the choice of taking their children with them, or leaving them with social services, and they did what any half decent parent would do. So they ended up given a "free flight" on a plane full of people being deported, which blurs the difference - but it's obviously there. The issue is that the parents were not granted access to legal counsel, though that's a consequence of expedited removal [1], which dates back to Clinton.
I think this issue mostly emphasizes the highly unpleasant issues that unrestricted bithright citizenship causes. There's a reason literally no other advanced economy, besides Canada, has maintained such a thing. [1] And Canada is probably the outlier there due to being geographically protected from illegal immigration. Even if somebody e.g. boats over to North America, they're going to be much more likely to head towards the US than Canada.
I say maintained because it's self evident that birthright citizenship would have been a given in the times before big government, if not only because it couldn't not be a given. But basically everywhere desirable started getting rid of it once it started being abused. The entry on Ireland, the last country in Europe to eliminate unrestricted birthright citizenship, is interesting:
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On 1 January 2005, the law was amended to require that at least one of the parents be an Irish citizen; a British citizen; a resident with a permanent right to reside in Ireland or in Northern Ireland; or a legal resident residing three of the last four years in the country (excluding students and asylum seekers) (see Irish nationality law).[64] The amendment was prompted by the case of Man Chen, a Chinese woman living in mainland United Kingdom who traveled to Belfast (Northern Ireland, part of the UK) to give birth in order to benefit from the previous rule whereby anyone born on any part of the island of Ireland was automatically granted Irish citizenship. The Chinese parents used their daughter's Irish (and thereby European Union) citizenship to obtain permanent residence in the UK as parents of a dependent EU citizen. Ireland was the last country in Europe to abolish unrestricted jus soli. (see Irish nationality law).[107]
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[1] - https://en.wikipedia.org/wiki/Expedited_removal
[2] - https://en.wikipedia.org/wiki/Jus_soli#