The developers of Breath of the Wild weren't precious about well-established Zelda mechanics. This is a Zelda game, after all, where you get all your important items within the first hour, the Master Sword is an optional find, and you can complete every dungeon in any order – or not at all.
That also means that a lot of Zelda's most iconic items are nowhere to be found in Breath of the Wild. The game's director, Hidemaro Fujibayashi, told Kotaku that the developers experimented with the hookshot and other classic Zelda items, including the flying mechanical Beetle from 2011's Skyward Sword, but that ultimately these items "had potential to detract from the gameplay." The ones that made the cut as runes accessible from the Sheikah Slate: bombs (both round and square), magnesis (for moving metal objects around), stasis (for freezing time), and cryonis (for creating blocks of ice), were ultimately concluded to be the items that "would draw out the fun of the game," Fujibayashi said.
But there's one more thing that should have been included, one that played best in the N64 era's Ocarina of Time and Majora's Mask: A musical instrument. Many Zelda games have provided Link with an instrument to play, usually with magical properties and puzzle-solving effects. But the ocarina was best for the creativity it inspired. You could bend any note to achieve other pitches, making it possible to do things like play the Kakariko Village theme within the game. Just think about what that would have looked like in Breath of the Wild.