Words are only vague indirectly, by virtue of having a sense that is vague. Child' is ambiguous between 'offspring' and 'immature offspring'. The latter reading of 'child' is vague because there are borderline cases of immature offspring. The contrast is further complicated by the fact that most words are also general. For instance, 'child' covers both boys and girls.
Generality is obviously useful.
If uncertain whether someone is 35, I can hedge by describing him as 'thirty-something'. Vague' has a sense which is synonymous with generality. This precipitates many equivocal explanations of vagueness. For instance, many commentators say that vagueness exists because broad categories ease the task of classification. If I can describe your sweater as red, then I do not need to figure out whether it is scarlet.