You have it backwards. It is not a restriction on the natural born subject (though it affects him,) but rather a restriction on right of the the alien to pass along property.
The natural born son of an alien may pass along his property, lands, etc. as any other natural born subject.
You appear to be grasping at straws, here.
But may NOT inherit, as English-born children of English subjects CAN. That's a privilege restricted to ACTUAL natural born subjects, NOT Blackstone's interpretation of "generally speaking" natural born subjects.
Blackstone needed to use the disclaimer "generally speaking" because he knew the rights and privileges of English-born children of aliens were NOT the same as those of English-born children of English subjects.
Blackstone deliberately used a disclaimer. I know it's hard for you to wrap your mind around that, but it is what it is... a DISCLAIMER.