We seem to have had a much more laissez-faire attitude toward immigration back then. That’s reasonable, given the difficulties of migration in those days, and the lack of any welfare state to attract parasites. Not to mention an expanding frontier and a culture that forced people to assimilate.
However, that attitude is legislative and a matter for the people to determine, not the courts. As time passed, we enacted more and more restrictions on immigration (until 1965, when we started going in the opposite direction out of misguided liberalism). Those laws weren’t applied retroactively, as that would constitute an ex-post-facto law. But we began to place limits on who could come in, and the idea that the concept of jurisdiction is outside the scope of the legislative branch can’t be defended logically.
Here is the crux of the problem:
The US must be able to assert full jurisdictional authority over every person on our soil except for diplomatic staff.
If we do not, we are creating a protected class of persons who can do whatever they want on US soil as long as they can dodge deportation.
In the case of the piece of dirt who executed those three Americans in Newark a few months back, we would not be able to prosecute him or put him on death row for his crimes - all we could do would be to deport him with a promise from the Colombian government (or Ecuadorian if they have ascertained his true citizenship yet) that he would be charged for his crimes.
This is not acceptable.
So we cannot, as a practical matter, exempt illegal aliens or their US-born children from US jurisdiction.
That effectively ties Congress' hands.
What is needed is border enforcement and a policy that says: "We do not care if you gave birth to a citizen child in the US. You are not a citizen and you are being deported. You can either take your child with you, or leave the child in foster care."
What is also needed is a revision of the 1965 Act that eliminates "family reunification" as a valid criterion for legal residency.
In this way, a child born into the US would either accompany his parents back to his country of origin or be left in foster care.
This would obtain between birth and age 18 - either accompany your deported parents or be placed in the foster system.
Once age 18 is reached, he would be an adult US citizen, but his parents would still be permanently subject to deportation if they returned.
Rather than mucking with the Constitution and US sovereignty, the best solution is statutes that eliminate having children as an immigration strategy.