This boils down to an "is Pluto a planet" debate.

We act as if some languages have "compound words" that can encompass entire sentences (subject & object attaching to the verb as prefixes or suffixes) while others don't form compounds, and most are somewhere in between. But these are all statements about lexicographic conventions and say nothing about the languages. In reality all languages are muddles sprawling across a multidimensional continuum, and they abso-frigging-lutely do n't sit neatly in such pigeonholes.

This is a great comparison. We're arguing about the definition of "word", and attempting to expand it to include edge cases where two words with separate meanings have a different atomic meaning when combined.

We could have a similar debate about whether common suffixes and prefixes should be regarded as individual words.

Much like "planets" don't really exist as a separate natural object, words don't really exist in natural languages. They are artificial concepts, and therefore we will always have edge cases.

I would argue that it is still a useful discussion, as it sheds light on the nature of language (or of celestial bodies), even if the definitions defy the same rigour as mathematical concepts.