Blackstone included a disclaimer because not all children of aliens born in the UK were NBS.
And you cannot understand law by reading sentence fragments. Sometimes you need to read paragraphs, or even pages. But in your case, we may need to provide animation...or really large crayons.
That's part of it. The other part is that Blackstone states shortly thereafter that English-born children of aliens CANNOT inherit from their parents. They DO NOT have that privilege. Blackstone had to qualify his statement with a disclaimer because the English-born children of aliens DID NOT have the same privileges as English-born children of English subjects.
That won't change no matter how many times you try to argue against it. It was a firm matter of English law.