Does the Zelda series need multiplayer? Well I would go with no, but it could do with it, if it's done right then you have a more prolonged and enjoyable experience.
I really hate the negative perceptions people have on online game modes and such, especially when it comes to games that might not necessarily need it. Yes, that game may not fit the mould for a competitive/cooperative game mode, but that doesn't rule out if it would be implemented. First of all, who does it hurt? One doesn't have to play it, if they would rather play the single player, then they can simply play that. Other players may be interested, so it's beneficial for them. I see online multiplayer, as a no lose scenario -- yes it might take up development time, but we as Zelda fans are used to this. In my opinion, it's just a bonus, it's whether it's a good or bad bonus, which is the true question.
There is something always interesting about games that may not have been built for online, for me it's these type of games, that could bring the most unique and best online experience. We are used to standard multiplayer games, why not something different? It's no lie that it would be a challenge for the developers, but it's what they are there for, I'm sure they could implement it somehow, if so wished.
I've had quite a few ideas to be honest, one of my first threads here was to do with a "separate" fighting game mode -- basically it would be accessible from the main menu as a separate mode of sorts. If online was an option then it should be a completely separate from the story, we play for the main mode, keep that, but make a side mode perhaps - that doesn't take away from the core experience. Anyway, I think Co-op is the best bet for now, we've seen it be used quite well in the Four Swords games, so a more advanced and polished mode for a wide multiplayer experience could be great.