To add to Y-L's comment, as opposed to the several hundred angles accessible with the control stick (see this diagram:
http://www.ssbwiki.com/images/a/a5/Directions.png), the D-pad would only allow you access to 8 angles. This means you won't be able to:
• DI in more than 8 directions (leaving you unable to optimally DI a lot of moves).
• angle moves such as Fox's or Ness' up-B in more than 8 directions (leaving you unable to sweetspot the ledge, or even reach the ledge at all in many circumstances where you would otherwise have been able to if you were using the control stick).
• wavedash at any angle other than straight down or 45° (significantly limiting your movement options, especially if you play a character which relies on wavedashing extensively, such as Luigi) as a result of not being able to airdodge in more than 8 directions.
• fast-fall while moving horizontally at all.
• perform full length ledgedashes at all.
• angle your shield at all, leaving you unable to shield drop at all.
Smash is very purposefully designed around analogue control, which is why the D-pad can't reasonably be used for movement. You technically could (using the sideways Wii remote), but it's so severely limited as to not be worth bothering with at all (unless you're playing very casually). This is one of several reasons why you never see Smash being played seriously on a fightstick (as they also lack analogue controls, as well as having other limitations).
D-pad movement is almost certainly never going to be given official support, and is extremely unlikely to be given unofficial support. Although I speculate that it would be technically feasible if you want to try adding such functionality yourself (or convincing someone else to do it).
If your computer can run Project M well using Dolphin, then you can use a Dualshock controller there if you want. However, if you ever plan on playing with other people on an actual console (where only Gamecube or Wii controllers will be usable), then I would recommend against it as you'll just have to relearn muscle memory and will have trouble adjusting when you do have to use a Gamecube/Wii compatible controller.