I have a similar situation in my family - Irish immigrants to Canada married and raised their kids there, but after the father died the mother kids moved to the US and they all remained here for the rest of their lives. Based on memoirs from a cousin of theirs who followed the same path, I think they might have said they were “from Canada”, but also would have said that they were “Irish”.
In other words, the questions “Where are you from?” and “What ‘are’ you?” may get different responses from people, not just in the past but also today.
Another example – a cousin’s ancestors include German-speaking people with Polish surnames (they were from Prussia, and considered themselves “German”), and Slovenian people with German surnames (who considered themselves “Austrian” – Slovenia was a part of Austria at the time).
Having said that, I do think tracking an ancestor’s actual citizenship at the time of emigration can be useful, because it might shed some light on the historical context of the the event. But I don’t think I would ever use such data to say anything like “I’m 16% Holy Roman Empire!”. 
Also, I realize that @DaveSch’s reference to DNA information was just to mention the use of attributes, but it reminded me of another point, which is that the DNA one inherits does not come in equal percentages from each ancestor in a given generation (except for the approximately 50/50 split for parental DNA), and in fact none at all from some ancestors.
