From having played Smash more this past year with friends far more than I would ever have liked to:
It's not a fighting game. For starters, a true fighting game should be directed between two players to move to the same established goal, whereas the design for Smash (no rounds, different degrees to "kill", etc.) does not cater to that. You can argue that some fighting games have it similar by adding different amounts of health to certain characters, but this is generally balanced out in other ways (such as Crimson Akiha in Melty; almost half as much health as the toughest character in game, but in the right hands can deliver an unbeatable combo-lock and just outright win the game). Further, it's not variable. In Smash, a person on any final destination map might be fucked at 120% while he can go well past 300% if he finds a good hiding hole on Temple.
Further, while you can just go straight final destination, and you can turn off items, this is you modifying the game to suit that purpose. You can turn on Skyrim and spend the entire game chopping logs and selling them to NPCs, and there are autists who do that. But the game is a (shitty) RPG, and not a lumberjack simulator. No matter how much you ignore the rest of the game to focus on one small fraction of it, that does not modify the genre of the game.
Also, while it depends on the individual characters to some degree, Smash does not orient itself towards powerful combat play. There's also the fact that, while you have the distinction between the various forms of A and B attacks, you don't have the light-medium-heavy set typical of fighting games. I may be mistaken here, but no character I played had a 90 or 180 or anything of that sort either.
With the exception of characters like Little Mac, and even that's stretching, there's also no meter mechanics of any kind to take into account, or any sort of way to consider the charging of ultimate attacks. All you get is the Smash Ball, which comes in the form of an item. The Final Smash power levels also fluctuate heavily, so you get some that are great, but others which can be nearly useless half of the time - or can miss, etc. It's a very different way of going about things.
That's all not to say that it's not fun, and I've honestly probably logged more hours into it than I have any actual fighting game because I can't find anyone else to play with except my roommate, but the feel of the game is far too different to compare them. Consider this - if you pick up any MMO, you can tell it's part of the MMO genre. Pick up Smash and play it without any modifications - base game, large group - does it feel like a fighting game?