'Cure' originally meant 'care,' not 'heal' — the same root gives us 'curate,' 'curious,' and 'sinecure.'
A substance or treatment that restores health; the act of healing a disease.
From Latin 'cūra' (care, concern, attention, management), from an uncertain PIE source, possibly *kois-ā- (care). The Latin word originally had nothing to do with healing — it meant 'care' or 'concern' in general. A Roman 'cūra' was an administrative responsibility, a source of worry, or an object of attention. The medical sense developed because
A 'curate' (parish priest) and a 'cure' (medical healing) are the same word. Latin 'cūra' meant 'care,' and a curate has the 'cure of souls' — spiritual responsibility for a parish. A 'sinecure' is literally 'without care' (sine + cūra): a paid position with no actual duties. Even 'curious'