I am dogmatic about this the same way I am dogmatic that, in a Euclidean geometry, two parallel lines never intersect. Or that 1+1 = 2 and it never equals three.
The drafters of the 14th extensively debated this exact question. The debate was robust, and it went on for many days, and they addressed all these issues. It was an intentional choice to make birthright citizenship available to everyone on US land. The exceptions are laid out specifically: an invading army, and diplomats. I have read this history. I do not know it, because that's very far from my areas of expertise. But you can easily find information on it. There is no shortage of materials on the internet.
Two things you are missing (among others, perhaps):
1. The drafters of the 14th considered immigration to be a good thing. And even better than immigration was new citizens born on our soil. Because the drafters understood that immigration was the country's greatest strength. It is what made America into the juggernaut of the 20th century. And plenty of people on the right understand this. They bemoan low birth rates, and the aging population . . . and then they turn around and say, "nah, THESE babies, we don't want." Hmm.
2. There are also interactions with other countries that have birthright citizenship. I believe, at the time, Mexico had birthright citizenship available only to persons born in Mexico (this has since changed; and note that I am no historian of Mexico so nobody should rely on my recollection here -- but the general point remains valid). So let's say a person leaves Mexico and comes to the United States (the borders were pretty fluid back then, and they weren't necessarily clearly demarcated), and has a baby. If that baby isn't a citizen of the US, and not a citizen of Mexico, then who? Is the baby a citizen of nowhere?
The Supreme Court has long deemed the lack of nationality among the worst things that can happen to a person. Right or wrong, that's how it has been viewed. Bet you didn't know that exile is the only punishment that the Supreme Court has held to be categorically a violation of the 8th. You can be put to death for crimes; you can be imprisoned; but you can't lose your citizenship. That's cruel and unusual.
So when you are asking, "did they mean to create this 'abuse'"? the answer is unambiguously yes. They did mean to it. They did not see it as an abuse. Nobody important in US history saw it as an abuse (not that I'm aware of) until very recently, when the white folks in the South decided to take their fight against non-white people to the browns as well as the blacks.
And that's all there is to say about this topic. There's a reason why the Reagan appointed judge was so harsh toward the government lawyers. Why he said it was the clearest legal issue he had to adjudicate in 40 years on the bench. Because this law is unusually settled. There are a few questions of law more settled, but not many. This one is foundational.
