This reads to me as a way for the authors of the amendment to narrow any potential loopholes in the protection of the newly freed slaves at the time. All persons born in the United States are citizens of the United States. However, this says nothing about whether or not you are a citizen of the particular state you were born in. So potentially, a state could deny equal protection under the law (protections under state law or infringe upon federally protected rights) if this clause mentioned "citizens", rather than "persons". "Citizen" could be misinterpreted or (mal-interpreted) to mean citizen of the state in question. Additionally, it could apply to a non citizen resident/visitor of a state. If I am a citizen of Pennsylvania and am I work in New York, New York must provide me with the same protections under the law as they would provide a citizen of New York. The 14th amendment did not have immigrant aliens in mind but rather was narrowly focused on newly freed slaves who were before it ratification citizens of no place at all. So when we speak of "aliens", we must keep in mind that while it applied to "aliens" today, it was not meant to protect the rights of foreign "aliens" in particular.
I find this argument a bit weak. Ratification of an amendment is a big process and I find it hard to believe that no-one realized the implications of the 14th amendment beyond it's impact on former slaves. People realized the implications, and went forward with the text anyhow. Otherwise, you have to assume that everyone involved was just completely ignorant to the implications of the text written as is, which is a claim you'll need to provide a great deal more backing for me to believe.
The 13th, 14, and 15th amendments were specifically written for the special case of newly frees slaves.
The 14th amendment was ratified in 1868. The total population of the US in 1870 was around 38 million. The total number of immigrants was around 2 million. The slave population was around 5 million.
The implications of the 14th amendment are clear today and they may even have been clear then. Nevertheless the most pressing, most politically salient issue was the newly freed slaves. In one day (the day after ratification) the United stares gained 5 million new citizens.
I would not be surprised at all if the people involved at what time were a tad bit myopic, with respect to the problem at hand.
It is an assumption of ignorance on a massive and universal scale that is beyond reasonable. There is too many people involved to assume this was not considered. It's the same problem as assuming the moon landing was faked. The position that noone involved considered birthright centizenship beyond slavery is ludicrous. All those state legislatures, all those senators, all those house representatives, all their staffs plus the best legal minds available to the office of the president and your claim is not a single one of them realized birthright citizenship would apply to people who weren't former slaves? That is a ludicrous amount of doubt in human imagination.
EDIT: In fact in 1860, the us census measured 4.1 million people not born in the United States. Is your claim honestly that while the census actively measured this, not a single person realized what birthright citizenship would mean for the children of those 4.1 million non-natives?