I think Miis should be a playable character... let me explain.
In story mode you should start off with your Mii with the basic moveset. As you continue throughout story mode you can unlock new movesets so you can customize your Mii. Choose each special move separately or from a set. The movesets won't be copies of existing characters. Some may be based on existing characters, but with a Nintendo gimmicky twist to them.
As for multiplayer, I think you should be able to battle with a Mii too. You can register a moveset to each Mii and choose whichever one you'd like. There could be a separate option to customize Miis for multiplayer battle where you can only use the movesets you have unlocked.
A good way to keep things fair would be to have every Mii have normal attacks, and only customize their specials. But you would choose from a 4-special move set, not being able to choose your B, up B, side B and down B separately. That way you can have a set with a good up-B attack, but the other 3 are weaker. Or a really powerful normal B move, but bad recovery with the up B. Or keep the basic moveset with balanced everything.
This way you wouldn't have everyone playing as Miis using the same combination of the strongest of each specials. It would be a preference.