Any answer to "why squaring?" that doesn't reference the usual Euclidean distance, even if indirectly via, say, the Pythagorean theorem, seems to be missing an

Any answer to "why squaring?" that doesn't reference the usual Euclidean distance, even if indirectly via, say, the Pythagorean theorem, seems to be missing an obvious avenue of (if I may coin an awful word) intuitive-isation.