I have my c-stick on regular attack for a couple reasons. His tilts, in my opinion, are very situational and it requires me to instantly decide when to use them.(for quickness) Plus, with the c-stick on attack, u can use his neutral-a by tilting the c-stick diagonally. It is much easier to fast fall AND use a nair at the same time! I find this very helpful when approaching as well as edge-guarding.
When using the c-stick can u?... idk what it's called so i'll describe it.
Zelda, for example, can jump in a direction diagonally and, using the c-stick (set on specials ONLY) tilt the c-stick the opposite direction from which u jumped. Zelda will use den's fire and drift opposite way from the direction which she used den's. (midair!)
I'm not sure if this works w/ olimar, but if it does, u could throw pikmen and fall away from your opponent at the same time, farther than u would normally land. That's the only advantage the c-stick set-up on specials could present to me.