I think the biggest problem with introducing a stick would be the inaccessibility. Basically, the reason most people think a version of melee modded with like, new Green Greens etc. would fail is because it's an exclusive, bothersome kind of thing to go through the trouble of getting.
It's really about exclusivity. Most people who start playing competitively remember playing the game in their childhood, because of how ridiculously popular this game was when it came out. They start wanting to get good, and go through the trouble of learning all the ATs and changing up which stages they play on. Then they go to a tournament and half the people there aren't even using the GC controller.
The player thinks that the time he'd spent playing the game as a kid/teen was irrelevant and that until he gets a hold of one of these personalized controllers his play will be inferior. The level of exclusivity the game presents to newer players is increased when they also have to look through threads about what kinds of controllers to pick up, what the pros use, what they should look for as a lefty, etc etc.
I threw together my own Smash stick mockup:
I think it's a little hard to have your thumb resting on Z by default, the hand shouldn't be angled that way. Z should be near the c-buttons, in a place where the thumb can easily and quickly reach to Z while resting in the center of the c-buttons.
Furthermore, for a pad, it would be easier to have your hand resting in a neutral position and build the controller around it, so the c-buttons should be angled more diagonally.
B, A, X, R is your current finger set-up.
Massive mentioned that the last two fingers are less dextrous than the first two, which is absolutely true, so I think a pad would need to be re-ordered.
I recommend X, R, B, A.
X is the first priority, because the jump button is used far more frequently than any of the other three. R second, because it's your powershield/L-cancel button. Because L is on the trigger, it must be saved for light shielding. B third, simply because A is only used for jabs (which feels like a "light" movement itself, so suited to a lighter, weaker finger), tilts, shield grabbing and if your character has a tether, nair.
I came up with this: