Throughout its long history, The Legend of Zelda has been quite varied in gameplay for the mainline series, yet the games are most often strictly single-player. For the most part, cooperative and multiplayer modes have been relegated to Zelda spin-offs and handheld games. It makes very little sense for Zelda to lean in to some sort of competitive multiplayer, but a proper co-op game could be a unique entry in the mainline series.
The Legend of Zelda: Tri Force Heroes is the closest the series has come to a mainline co-op game, but it feels like more of a novelty because of its level structure. Up to three players can assume the role of brightly colored Links, and play through sets of levels, each with their own enemies, bosses, and puzzles. While Tri Force Heroes is an entertaining exercise in teamwork, it's missing the explorable world and traditional dungeon set up of most Zelda games.
Using a Game Boy Advance and a link cable, the original GameCube version of The Wind Waker let a second player control the Tingle Tuner item, which would allow the player controlling Link to find special items. This feature felt like more of an afterthought than anything, just like the ability for a second player to use motion controls in Super Mario Galaxy to pick up star bits. Nintendo has a notoriously lukewarm track record on multiplayer implementation, but there's a lot of potential for the Zelda series to deliver an incredible co-op experience.
A Co-Op Zelda Would Bring Some Novelty
It's quite impressive that the Zelda series has remained so varied in its gameplay and aesthetics over the years. A full two-player game, though, would be entirely new territory. The other, top-down co-op Zelda titles have players controlling clones of Link, but a narrative-heavy mainline title could use another playable character, such as Zelda, in order to really stand out. Two characters with different fighting styles or weapons could contribute to replayability, and spice up combat with interesting combos.
Two players in the game would also necessitate completely new dungeon design. Puzzles could be more intricate, requiring communication and good timing. Whole dungeons could even split the players, with one's actions effecting the other half of the dungeon, or tie the players together so they can't travel a certain distance from each other. Novel enemies could be introduced that require a certain combo of items to defeat, or some that have to be distracted so that the other player can get to a weak point. New Zelda boss battles would have to be invented to compensate for a second player (a floating head could have four hands with eyes in the palms this time).
It's understandable why Nintendo has kept its third-person Zelda titles single-player. The series has a sterling reputation for delivering long, intricate solo campaigns. Additionally, a co-op game might potentially be taxing on Nintendo's usually below-average hardware specs. Requiring co-op could also affect sales, a risk Nintendo might not be willing to take with The Legend of Zelda, but the series is ripe for a co-op campaign nonetheless.