But if a definition works well enough in practice to point out the intended empirical cluster, objecting to it may justly be called “nitpicking”.
You should probably put in a disclaimer excepting mathematics from this—assuming that you agree it should be excepted. (That is, assuming you agree that “Aristotelian” precision—what mathematicians call “rigor”—is appropriate in mathematics.)
“Definition” has a different definition in math.
Mathematics is largely already excepted from the above discussion—this post is talking about empirical clusters only (“When you draw a boundary around a group of extensional points empirically clustered in thingspace”), and mathematics largely operates in a priori truths derived from axioms. For example, no one needs to do a study of triangles to see whether their angle all do, indeed, add up to 180 degrees—when that’s not part of the definition of triangles, it follows from the other definitions and axioms.