And if I were there for Diogenes's chicken caper my eyes would have been a-rolling...

Science is only one facet of life where definitions are important, and arguably not even the most daily impactful.

Also science is one of the few arenas with any real interest in a rigorous epistemic framework so that same concept of advancing definitions doesn't work with social values, political situations, and most media where definitions are changed or co-opted for convenience and leverage rather than objective rhetorical value.

Pretending they do leads to things like 'we will become more progressive over time as a society' being accepted as truisms of human nature instead of the long-term efforts of hundreds of thousands of highly motivated and violently targeted individuals working to better the world for people they will never meet.

So yes, rigorous definitions in science is important, and thankfully we have developed many useful frameworks to ensure that no matter where in the world scientists share knowledge that it can be held to certain standards of rigor and objectivity

Literally no other facet of life has that same kind of special protection.