Super Smash really does need the analog stick...that's why it's called a "Smash" move.
Unless they changed the gameplay, which honestly I wouldn't mind, it would need to use the touchpad to do certain smashes, or just abandon a lot of moves.
Let's say you want to punch forward in SSB.
You can press A. That does a weak forward punch that usually combos about 3 times, culminating in a third, stronger punch.
Or you can press forward (right/left) on the analog stick and A at the same time. This will give you a moderate punch forward, significantly stronger than a standard A punch.
Or you can smash forward (right/left) on the analog stick and press A at the same time...smashing is a very quick tap. This gives the strongest punch...the punch that will likely knock someone off the screen.
The advantages to using weaker punches and kicks is for more fluid motion. You can jump over someone, smack them down in mid-air, do a smash-down move, then perhaps a weak in-air A kick, then perhaps another smash-down move...etc. The game would be too bulky and slow if the only moves available were smash attacks.