In reference to Alice being a Princess in Kingdom Hearts, I think that was meant to be a reference to her purity of heart. Think about this: Ariel, who is a princess, was not a Princess of Heart. I guess it makes sense somehow in the context of the game. (Mainly in that it works to have a Wonderland level in the game. Heheh.)
As for the new princess not having enough on her shoulders, I think that's really hard to determine at this point, unless you all know something I don't. I mean, the movie hasn't come out yet and I know I at least don't know what's going to happen.