I think it's just not a conventional fighter.
You have to remember that the point of the game is not to inflict damage, but to shove them off the screen. In this case, I feel it redefines the genre. Most other Beat 'em ups are all about punching and kicking and pulling off the moves successfully and quickly, but Smash Bros is all about fighting in any way you can - throwing things at enemies, strategically making sure they cannot get back on the stage, using everything to your own advantage. It's made a little harder, when you take into account the triple jumps that characters can use to get back on the stage. The game is also incredibly easy to handle, it's just knowing the best tactics (which admittedly won't work for everyone) and what to do to win. Also the fact that it's 4 player means that you can literally be the best by KOing all three of your opponents.
In the end, it's just not the kind of beat 'em up you'd expect. No blood, no combos, no secret moves, just straight forward bashing and removing your opponents from the screen. (It would certainly make Jerry Springer more interesting if they had guests being thrown of the stage in such a manner, I can imagine one person doing a smash attack so powerful it make even Jerry fly out of the set).