Abel Blood, Jr. of Hollis was born on 5 May 1791 or else he was not. There is no narrative, no scenario, no jaw-droppingly brilliant insight like the complete specification of the past is impossible (so, too, the present and so, too, the future. What of it?). The related yes-or-no question seeks objective information, and the complete specification of the smallest hypothesis set responsive to the question is also objective ({he was born that day, he was not born that day}).
Subjectivity sets in quickly. It may be
useful to choose to examine a richer responsive hypothesis set (a calendar of the 1790's, for instance). The trade-off between specificity and plausibility which can define "choices according to usefulness" is subjective.
If I choose a richer hypothesis set, then which one? (The 3600+ days of the 1790's are not all seriously possible, perhaps a smaller set of days will serve, or maybe a different granularity altogether: really all I care about is any day in 1791
versus any day in 1796, and if neither of those, then maybe I need to reframe the problem - I could be getting confused by traces of the Abel Blood who was born, by all extant accounts, in nearby New Ipswich, New Hampshire on 27 June 1791).
And then there's the subjective weight given to the pieces of the available evidence. Ah, at last, a role for a "scenario." One line of records favors 1791 (in black letters, an official state document, but a handwritten copy of something antecedent which may or may not be extant) while a distinct line favors 1796 (literally set in stone, but on whose say-so?). Not that this kind of thing is rare in genealogy, but still - how in hell did that happen? Depending on different ideas about how to answer that question, different weights will be given to the two lines of traces. A judgment call, and so subjective.
The report is due soon. As with Jesus, there is little chance that further evidence bearing on the life dates of Abel Blood will emerge anytime soon. Unlike Jesus, I have enough evidence in hand, contradictions and all, to assert "it is not seriously possible that this Abel Blood was a fictive character" with high confidence that few will disagree. So: "Abel Blood, Jr. (1791 or 1796 to 1867)" it will be.
There are many other questions that can be asked about Abel Blood, Jr. Some of those will have no objectively determined responsive hypothesis set (for example, How did the American Civil War affect his life?). much less an objectively correct answer. No worries. There are other techniques available for those questions besides the ones that genealogists use, and other conceptions of "relevance" to organize the available evidence in trying to answer the questions.
Whatever works is nearly Bayesian. It's all good.
How objective or subjective can a classification system be?
In general, classification systems are adopted for their usefulness, although each classification within the system may be objective. For example, a bat is objectively a "flying animal" but whether "flying animal" is a useful category is a subjective matter, probably depending on both personal judgment and circumstances.
Can it be improved?
Useful classification systems would likely not be unique for the collection of elements being classified. While it is possible that one adequately useful classification system might be "uniformly better" than another (Pareto preferred on all dimesions of preference), it is happenstance whether there exists some unique classification system that dominates all others. Barring happy happenstance, then, system choice will be based on trade-offs and so thoroughly subjective.