Consider the following sentences and what sets them apart:
Vicar of the parish, Josiah Jones, had skipped church that Sunday
to get roaring drunk.
Vicar of a parish, Josiah Jones had skipped church that Sunday to get
When we leave out the comma after Josiah Jones in the second sentence it is because "Vicar of a parish" is clearly merely an attribute of Josiah Jones; it is not the subject of the verb, and is not standing in apposition to Josiah Jones:
We can't say this (not really):
Vicar of a parish had skipped church that Sunday to get roaring drunk.
That wouldn't make much sense as it is so broad and vague. It would be like saying "CEO of a corporation had missed a meeting that day." "CEO of a corporation" is a descriptor.
In the first sentence which begins "Vicar of the parish", it is implicit that we had been speaking earlier about the parish. The definite article says so; it requires an antecedent and without one the story is beginning in medias res. In the second sentence, there is no implicit antecedent.
You are contending that "Washington's grandfather" could be regarded as merely an attribute of the subject, John Washington, and not itself the subject of the verb, although the phrase can stand equally well as the subject of the verb:
Washington's grandfather had sailed from England to North America after being granted land by King Henry VIII.
What militates against your view is this: generally, when we are talking about someone, our topic, and then change the focus to one of their forebears or to a sibling, say, in order to give further information about our topic, we normally treat the two noun phrases, the family relationship and the name, as apposite, and treating them as inapposite sounds "off" because doing so is tantamount to a change of topic, not an elaboration of the topic.
Which sentence would you prefer here?
Abel's brother, Cain, was the elder of the two. apposite
Abel's brother, Cain was the elder of the two. inapposite
We had been talking about Abel, implicitly, or once again we would have a statement made in medias res. The inapposite version makes Cain a new topic, and thus it is non-sequitur.