The impunity with which the disloyalty of today is rewarded is one reason the people of today lack the commonsense to understand the starkly simple linkage between loyalty, allegiance, and citizenship.
Why was it unnecessary? The English common law definition of "natural-born subject" differs significantly from de Vattel's "les naturels ou indigènes." "Natural-born subject" allowed for jus soli, whereas "les naturels ou indigènes" was strictly jus sanguinis.
The Founders were familiar with both English common law and de Vattel. They could have made it clear that they were following de Vattel's "les naturels ou indigènes," but they did not. Given that de Vattel himself never used the phrase "natural-born citizen," you need to argue that "les naturels ou indigènes" means that, and it is not obvious that it does. By contrast, at the time of ratification, English common law had a well-defined concept of "natural-born subject" in the English language. I need only argue that "natural-born subject" became "natural-born citizen," which is easier to do because the phrases are identical except for the system of government (monarchy vs. republic).
Anyone with half of a brain knew a person was born with the father's allegiance, hence natural born allegiance and natural born citizenship that goes along with the allegiance.
But there were a lot of "anyone[s] with half of a brain" who lived in 1788 who were "natural-born subjects" of the British Crown prior to 1783, and "natural-born subject" included children of aliens who were not diplomats.
Obviously, you like de Vattel's definition better than the English common law one. But what you like is not relevant here. The question, as I've repeatedly stated, is what would a reasonable person in 1788 have understood "natural-born citizen" to mean? If he had been a "natural-born subject" of the British Crown up to 1783 and he knew that "natural-born subject" was defined in English common law to include children born to non-diplomat aliens, then it's a stretch to argue that "natural-born CITIZEN" takes on the definition from a specific French-to-English translation of a Swiss legalist's writings.
de Vattel's definition indeed may be more "natural" to you. If that's the case, then you're expending effort on the wrong issue. Barack Hussein Obama II is a "natural-born citizen" as explained by Justice Gray in Wong Kim Ark. You don't like that because he only had one citizen parent. You're well within your rights to not like that, but then you should be clamoring for a Constitutional amendment to make our nationality law closer to that of Switzerland, or even stricter, not arguing that BHO II isn't a "natural-born citizen" by a Swiss legalist's definition.
Why do I say "stricter"? Even if we had a nationality law like Switzerland's, BHO II would still have been a "natural-born citizen" because his mother was a citizen. For BHO II to not qualify as a "natural-born citizen" under the more restrictive Swiss criteria, you'd have to abolish jus soli and restore patriarchy.
Switzerland recognizes that there's one problem with patriarchy; absent a paternity test, you can never be sure who the father is. But if you left your mother's womb, you are your mother's child, and hence, at minimum, you should take on your mother's citizenship. That is why a child born to a Swiss father and unmarried non-Swiss mother does not automatically have Swiss citizenship; the father has to acknowledge paternity, or a paternity test has to show that he is, in fact, the father.