The US has never permitted the exercise of foreign jurisdiction upon foreign nationals within the US except for diplomats. That being the case, the exclusivity of US jurisdiction upon people within its borders, legally or not, has long been a matter of law.
So, basically my point. Other countries don't
have jurisdiction over people while they're in the US, aside from diplomats of course. Thus the whole claim that other countries somehow have jurisdiction over someone born in the US is shown to be false. But even if they did, it wouldn't mean the US doesn't have jurisdiction, which it does.
I don't think we can say they were necessarily "going for more than that" because they didn't say more than that. Given the historical context, they may well have not seen a need to be explicit about exclusivity: "What else would we be talking about in this time and this place?"
This doesn't make sense. The phrasing very clearly goes well beyond the slaves, as shown by the fact that, again, there's nothing about slavery mentioned, even obliquely. Far more people than just slaves are subject to the jurisdiction of the United States.
But, even if we set aside the text and talk just about motivations, we can very clearly see they had more than just slaves on their mind.
In the discussions of it in the Senate, it is made very clear that it applies to a whole lot more people than slaves, as shown especially by the argument between the Senators Cowan and Conness, because Cowan was fretting about it being a bad idea to extend citizenship to children of immigrants. No one said Cowan was misunderstanding it, and the response to him by Conness was merely that Cowan was overstating the dangers.
So let's take a look at some statements by Cowan. After going on a rant about Gypsies, he then complains:
These people live in the country and are born in the country. They infest society. They impose upon the simple and the weak everywhere. Are those people, by a constitutional amendment, to be put out of the reach of the State in which they live? I mean as a class. If the mere fact of being born in the country confers that right, then they will have it; and I think it will be mischievous.
This isn't in reference to slaves. Then after also fretting about Mongolians, he concludes with:
Therefore I think, before we assert broadly that everybody who shall be born in the United States shall be taken to be a citizen of the United States, we ought to exclude others besides Indians not taxed, because I look upon Indians not taxed as being much less dangerous and much less pestiferous to society than I look upon Gypsies. I do not know how my honorable friend from California looks upon Chinese, but I do know how some of his fellow-citizens regard them. I have no doubt that now they are useful, and I have no doubt that within proper restraints, allowing that State and the other Pacific States to manage them as they may see fit, they may be useful; but I would not tie their hands by the Constitution of the United States so as to prevent them hereafter from dealing with them as in their wisdom they see fit.
So it is fairly obvious that, yes, we are seeing far more people than just slaves being covered by it, which is
exactly why Senator Cowan opposed it.
Lest anyone claim that he was wrong in his interpretation, we may note that
no one objected to his interpretation of what the Citizenship Clause did. The point raised against him was not that he was wrong about children of Gypsies and Chinese being citizens, but that there wasn't any reason to
worry about the effects he described of granting them citizenship. Senator Conness (the "honorable friend from California" he refers to) defends the idea of granting them citizenship, saying it's not something to worry about, focusing particularly on the Chinese. Here's a particularly relevant excerpt:
The proposition before us, I will say, Mr. President, relates simply in that respect to the children begotten of Chinese parents in California, and it is proposed to declare that they shall be citizens. We have declared that by law; now it is proposed to incorporate the same provision in the fundamental instrument of the nation. I am in favor of doing so. I voted for the proposition to declare that the children of all parentage whatever, born in California, should be regarded and treated as citizens of the United States, entitled to equal civil rights with other citizens of the United States.
Why all this discussion about Gypsies and Chinese and others if it was just about the slaves? The answer is easy: It wasn't just about the slaves. It was never just about the slaves. The Citizenship Clause was meant to be applied far more broadly than that. Again, we know that because that's literally what they said.