The grass radical 艹 declares medicine's origin: herbs. Traditional pharmacology was botany — roots, barks, and leaves decocted into bitter soups. 药 is the plant kingdom signed up (约) to heal you.
良药苦口 'good medicine tastes bitter' excuses every foul decoction and every harsh truth. The TCM pharmacy with its hundred wooden drawers is 药's cathedral; 中药 herbal medicine and 西药 Western pills coexist in most Chinese medicine cabinets without contradiction.
Herbs 艹 under agreement 约 to cure you — MEDICINE.
Chinese 'takes' medicine by eating it — 吃药 'eat medicine' — even when it's a liquid. The verb never changed from decoction days.