I remember reading in another smash 4 thread that when it's set to smash and you are aerial, it mimics the input of
+
instead of just performing the smash which when using f-air and b-air will push your momentum that way. If you don't use the c-stick for aerial often, you might not notice it much since a similar effect you are already adapting to from using the left stick for it. When the left stick is attack, there is no loss of movement when aerial.
Personally I don't use the c-stick as much for tilts and aerials either, but when on the Wii U I remind myself of a few uses where it excels. Mostly with spiking, as I can short hop over an opponent and stage spike them for a nice surprise without losing my momentum or accidentally fast falling will hitting my target with the sweet spot of Ragnell.
I've read of other players that have trained in using the shoulder buttons for jumping, and rely specifically on the c-stick for attacks. I haven't been that committed to attempting it since I've got some 15 years of experience the other way and unlearning that would take too long, but it's a good place for debate on the merits of such a layout for smash.