The so-called principle in England that allegedly made those born of 'aliens' to be natural born subjects was in reality an act of naturalization sparked by a change of monarchs and decided in an ensuing court case.
"With the end of the Tudor dynasty following the death of Elizabeth in 1603, James VI of Scotland inherited the throne of England as James I, thereby uniting the two kingdoms in the "union of the crowns." At once there was considerable debate concerning the extent of union effected by the succession of the Scottish King to the crown of England. James, however, considered a regal union alone to be insufficient. Upon his arrival in England, James advocated a closer unity between the laws, institutions, economies, and churches of England and Scotland to protect and strengthen the Stuart dynasty."
"All but two of the justices determined that persons born in Scotland after the accession of James to the throne of England (the postnati, as they were referred to in the case) were to be regarded not as aliens in England but as natural-born subjects, qualified to inherit English land. The postnati as subjects born into the allegiance of James after he became King of England owed their allegiance to the sovereign of England as well as Scotland. By constrast, the antenati, those born before 1603, were born into the allegiance of a King with no relation to the English throne. Therefore, unless the antenati were naturalized by statute, these Scottish subjects of James remained aliens as a matter of English law."
As you can see, the 'aliens' in question weren't simply random foreigners or immigrants, but those who were part of what we know now as the United Kingdoms.
"Several accounts of Calvin's Case were published, but by far the most influential was that of Sir Edward Coke, Chief Justice of the Common Pleas. Coke's published reports were widely accessible to lawyers of later ages, and Coke's report of Calvin's Case was the first comprehensive statement in England of the law of naturalization. Calvin's Case established a territorial rule for acquisition of subject status at birth:
"Every one born within the dominions of the King of England, whether here or in his colonies or dependencies, being under the protection of--therefore, according to our common law, owes allegiance to--the King and is subject to all the duties and entitled to enjoy all the rights and liberties of an Englishman."
If that last paragraph is a direct quote of the law, then it doesn't specifically declare anyone to be a natural born subject. And it was called a naturalization law. This 'common law' is what allowed American colonists to be considered natural born subjects as this rule affected those born in the dominions and under the protection of the King. This didn't apply to what we think of as aliens, which in their time, were foreigners or denizens. We know this because the charters of some of the original American colonies say so.
"Also, Wee do for Us, our Heires, and Successors, declare by these Presents, that all and every the Persons, beinge our Subjects, which shall goe and inhabitt within the said Collony and Plantation, and every of their Children and Posterity, which shall happen to be born within the Limitts thereof, shall have and enjoy all Liberties, and ffranchizes, and Immunities of free Denizens and naturall Subjects within any of our other Dominions, to all Intents and Purposes, as if they had been abidinge and born within this our Kingdome of England, or any other our Dominions.
Charter of the Colony of Massachussetts - 1620"
Here it's saying you can be born in the province and enjoy the liberties of free denizens or natural subjects. Similar language is in the charters of Georgia, Rhode Island, Maryland and Maine, etc. Whatever common law we were allegedly following, did not specifically declare all persons born in America to be natural born subjects. In most of these, it clearly reserves the declaration of being a natural born subject for those who are born of subjects. In some charters, foreigners were required to take an oath of allegiance and were allowed to become denizens or subjects, which would be akin to naturalizing, thus any children born thereafter would be different than the situation in Wong Kim Ark. The Wong decision evidently oversimplified the laws or relied on citations that blurred the common law. Whatever you think is a guiding principle or 'natural allegiance' just isn't so.
Now that same principle of “natural birth” allegiance (no matter how well founded you think the concept is) to the nation of birth was extended to Wong Kim Ark; but he was not a “natural born subject”, he was a citizen - but where did he lose “natural born”?
Of course he, by the findings of the Court, did not lose his “natural born” allegiance to the nation of his birth.
If born in England he would, by the law cited, be a “natural born subject”. The same principle, extended to his birth in America, would make him a “natural born citizen”.