I think your argument may be a little too strong. Would you refrain from discussing, say, happiness, sadness, etc. in your daily life without a formal definition of what happiness is exactly at a structural level? And I say that as someone interested in formalizing ethics, and formalizing all of those notions. The point is, to even (ideally, formally) define them we need intuition and intuitive discussions about what their definitions should be, and we are still at (very) early stages of what could constitute a real formalization.[1]

More significantly, the utility of those concepts far precludes scientific definitions, those terms have been useful for thousands of years, and are essential to human society!

(Again, certainly not against definition, but be mindful of being too strict, too soon about it :) )

[1] The benefits of formalizing (human concepts) are subtle: like formalization in math, they help us build confidence that we're not building sand castle, dig deeper into theories of meaning, and use this to slowly improve lives of everyone. But like math, we've been doing it informally for very long, and a strict axiomatic formalization is still today relatively rare (although progressing with the aid of computer proof systems) for most fields. Still, the evolving standards for proof are likely essential for many of the deep theories we've achieved (probably including say modern logic and Godel's theories, algebraic geometry, functional analysis, etc.).