Do words have intrinsic meaning? No.
The meaning of words is negotiated constantly (and mostly unconsciously) within a community. That’s why meanings change. Meaning inheres not in the word but in the community, because language as a code inheres in the community. Where by code, I mean a mapping of forms to meanings, which enables you to be understood by other members of the community. And the community, over time, can and does change its collective mind about those mappings.
But language is also individual. Individuals learn the code that is out there in the community, and build their own internal representation of it. In fact, the community version of language is an abstraction, an aggregation over individual languages (idiolects), the real languages inside people’s skulls.
That abstraction is still important, though. If you start using words like Humpty Dumpty, to mean whatever you want, you go against the community norms of the language. Which means concretely that you go against the norms that most if not all members of the community have internalised.
Does it make sense to argue over the definition of a word? Yes.
The change of meaning in words is most of the time unconscious and gradual. But especially in literate and specialised societies, people become aware of meaning change. And people have a stake in defending the stability of a word’s meaning in a particular domain. If that domain has gatekeepers, is reasonably small and well codified (as is the case with jargons and specialist vocabularies), they’re likely to succeed.
And even if they don’t, meaning change is realised at an individual level, from one person to the next. Sometimes (particularly when you haven’t been paying attention), you will be ambushed by a meaning change. Like contemporary teen lit. (Sophia de Tricht: my surprisingly non-teen source of teen slang here.) Sometimes confusion will result, and a negotiation will happen.
And of course codified literate language is subject to prescriptive forces. In general usage, those forces have less power over word meaning than they do in specialist contexts. But people still do care what the dictionary definitions of words are, and they still argue over them. That’s now part of how the community negotiates the community understanding of words.