Thinking such as yours is why our Constitution is deader than fried chicken.
Those of us who cherish it, like the author of this excellent piece, will continue to fight to return it to authority.
Vattel is not the law. The constitution -- as written, not as informally amended by FR posters, statutes, treaties, and court decisions of the US are. Persuade a Federal court that NBC must be understood as Vattel describes it, then get back to us.
Until then, the operating precedent is English common law, which recognizes jus soli as sufficient for NBC status, and and the Wong Kim Ark decision, which incorporated that common law precedent into American jurisprudence.