I don't agree with the assumed equivalence between precision and objectivity. Language can be precise when describing a subjective perspective, and it can be imprecise or ambiguous when describing objective facts. The tendency toward increasing precision is a good thing, in my opinion. If anything, precision in language allows writers to tell better, more nuanced stories about subjectivity.
Increasing precision is good to the end that is disambiguation. The problem is that that end is not always what language is good for. Metaphor is an incredibly useful tool, because it allows us to convey meaning with imprecise definition, but precise implications.
The meaning of an expression is its implication, not its definition. The implication must be decided by the reader. This is either done by strict definition, or by arbitrary inference. Inference is a powerful feature of language, because it expands the set implications that can be expressed without abstracting the language. Without inference and metaphor, we must instead create a tower of well-defined abstractions that rule over us; having already determined what implications are relevant: objective truth. With inference and metaphor, the writer/speaker can articulate their implications with familiar language; relying on the reader/listener to infer from the expected relevant perspective: subjective truth.
Essentially the tradeoff isn't whether or not you get precision, but whether that precision can be shared by the writer and the reader, or be managed entirely by the writer. Defined abstractions allow the writer to be unambiguous to anyone (objective), while inference allows the writer to offload that responsibility to the context and perspective of the reader (subjective).
Does that make sense?