It would be a really neat idea, and I would definitely play it, but I see one or two problems that will keep it from ever happening.
I'm looking to World of Warcraft and how it has affected the Warcraft franchise.
After WoW came out and blew up into the most successful MMO ever Blizzard went from being a strong, multi-franchise, developer to being a developer that is 95% dedicated to supporting just one game (and the other 5% focused on a few side-projects). Nintendo would have to pump so many resources into properly supporting an MMO that either it would have to be spun-off into it's own division/company or it would consume nearly all of Nintendo.
Since WoW was released there have been no new Warcraft games (expansion packs don't count). WoW has completely consumed the entire Warcraft franchise. Obviously, I can't see into the future and neither can anyone else, but I think most reasonable people can foresee the end of WoW's life cycle will be: WoW will go until it has jumped the shark and has been completely dragged into the ground. After that eveyone will be so burned out on Warcraft that it will be very likely that there will never be another Warcraft game ever made. I don't want to see the Zelda franchise get stalled or killed by one single MMO.
Now, all that being said... I think a non-canon MMO based on Super Smash Bros would be brilliant!
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A neat idea that could be impleneted as well, that would be somethign different than I've seen with a lot of other MMOs, would be to have players choose a faction (which is independent of race or class, and race/class combination could be any faction) that go back and forth between allying and waring against each other based the story of each quest chain.
Desciples of Wisdom
Patron Deity - Nayru
Believes in Diplomacy. Subscribing to a philosophy of pacifism, Desciples of Wisdom prefer to talk problems out and saves violence as a last resort.
Desciples of Courage
Patron Deity - Farore
Believes in Justice. Desciples of Courage believe in defending the weak, they tend to evaluate each situation they find and go with their gut instinct to decide what is right and wrong.
Desciples of Power
Patron Deity - Din
Believes in Power. Desciples of Power believe might makes right. If someone weaker than them has something they want they want Desciples of Power will fight to get it.
Desciples of Chaos
Patron Deity - Majora
Believes in Freedom. Desciples of Chaos believe all people should be free to find their own destiny and resist any form of tyranny, authority, or organized government.