A lot of characters have 4 useful special moves, and only a few characters have special moves that aren't somewhat useful at least.
Luigi, Diddy Kong, Wario, Link, Toon Link, Zero Suit Samus, Pit, Ice Climbers, Kirby, Olimar, Fox, Falco, Wolf, Ivysaur, Charizard, Marth, and Sonic off the top of my head have four specials that are all very useful to them. A few others like Snake are debatable to be included in this group (I'm not sure how useful the Nikita really is), and then you have guys like Ike who have 3 obviously useful ones and a fourth that's nice to have but not actually worth using all that often (if only Ike had Marth's Counter...). I actually am not that sure about including Bowser in the 4 useful specials group on account of Bowser Bomb being a pretty limited move, and I've seen some players with very good SDI who seem to make Fire Breath into a move that isn't very good.
The main reason using only special moves is a bad idea isn't that special moves are bad so much as limiting yourself to 4 moves is really limiting no matter how good those moves are...