I think the answer is probably “No”. I don’t see how our country can deport people legally declared citizens.
Children are wards of their parents. They can come back (if they want) when they are 18.
You give the parents a choice. If they abandon their kids here, they are banned from ever applying for citizenship or re-entry because of child abandonment. We take the kid and put him into foster care. It’s worth it if it coincides with overturning birthright citizenship to end the problem from this point on.