No. You're reading into it what you want it to mean.
Children born in England to aliens could NOT inherit property, holdings, etc., from their parents. Children born in England to English subject parents could. So while Blackstone may choose to say that "children of aliens, born here in England, are, generally speaking, natural-born subjects, and entitled to all the privileges of such," the fact remains that there indeed were significant differences in the rights and privileges of each. That's why Blackstone deliberately uses the disclaimer, "generally speaking." He knows they were not the same, as should you.
“Children born in England to aliens could NOT inherit property, holdings, etc., from their parents. “
Proof?
“So while Blackstone may choose to say that “children of aliens, born here in England, are, generally speaking, natural-born subjects, and entitled to all the privileges of such,” the fact remains that there indeed were significant differences in the rights and privileges of each.”
Proof?
Many of the original cases involving NBC were ones of property, and I can’t recall any that hinged on if the NBC/NBS had alien parents or not.
Lynch, for example, was born in the USA of English parents visiting here for a few months - but she was declared a NBC.
Blackstone hedged with “generally speaking” because there were exceptions, such as ambassadors.
By the common law of England, every person born within the dominions of the Crown, no matter whether of English or of foreign parents, and, in the latter case, whether the parents were settled or merely temporarily sojourning, in the country, was an English subject, save only the children of foreign ambassadors (who were excepted because their fathers carried their own nationality with them), or a child born to a foreigner during the hostile occupation of any part of the territories of England. No effect appears to have been given to descent as a source of nationality.
Cockburn on Nationality, 7.
The English statute of 11 & 12 Will. III (1700). c. 6, entitled
An act to enable His Majesty’s natural-born subjects to inherit the estate of their ancestors, either lineal or collateral, notwithstanding their father or mother were aliens,
enacted that “all and every person or persons, being the King’s natural-born subject or subjects, within any of the King’s realms or dominions,” might and should thereafter lawfully inherit and make their titles by descent to any lands
from any of their ancestors, lineal or collateral, although the father and mother, or father or mother, or other ancestor, of such person or persons, by, from, through or under whom
title should be made or derived, had been or should be “born out of the King’s allegiance, and out of is Majesty’s realms and dominions,” as fully and effectually, as if such parents or ancestors “had been naturalized or natural-born subject or subjects within the King’s dominions.” 7 Statutes of the Realm, 90.
You are conflating who was natural born with inheritance laws. Talk about reading into it what you want it to mean!