They removed the ability to equip them. The medallions were originally equippable both to your items as well as being equippable to your arrows.
The items in the game are remnant of that:
Dins Fire -> Fire Medallion
Farore's Wind -> Wind Medallion
Nayru's Love -> Shadow Medallion
As well as the elemental arrows, where you'd equip the medallions to your bow:
Fire Arrow -> Fire Medallion
Ice Arrow -> Water/Ice Medallion
Light Arrow -> Light Medallion
The Shadow Temple is actually one of the older temples in the game. That's why, if you look down at the entrance of the Shadow Temple at the pedestal where you're supposed to use Din's Fire, there's the Fire Medallion emblem. It's also why you can freeze Bongo Bongo with the ice arrows even though you don't get the ice arrows until the Gerudo Training Grounds, since you were supposed to already have beaten the Water Temple and thus have the medallion to equip to make ice arrows at that point.