The showy flowers are sterile
A wild hydrangea head is a flat plate of tiny fertile flowers, dull and hard to see, ringed by a handful of large flat showy ones. The big ones around the edge are sterile. They have no working pollen and no ovary. Their entire job is to be visible from a distance and steer an insect into the middle, where the real flowers are.
That is the lacecap, and it is the original. The mophead everybody pictures is what happens when that arrangement is pushed to its limit by breeding, so that nearly every flower in the head has become a large sterile one and the fertile flowers have all but vanished. A mophead hydrangea is, in the plainest sense, a plant that has been bred into being almost entirely advertisement.
Look closely at what those showy flowers are made of and they are not petals either. They are sepals, four of them, in tissue much thicker and tougher than a petal.