I agree that Twilight being dubbed princess the same day she became an Alicorn was more than a bit hasty. Especially since, like Cadance, we didn't actually see her doing anything overtly Princess-y for quite a while, and she didn't even a freaking domain to be Princess OF for quite a while.
Plus, I feel it's a bit silly for all alicorns to automatically become princesses.
I don't doubt that Twillight can do it, but she still doesn't exactly seem interested in the development, and while it was strongly implied that Twilight was always intended to become Celestia's replacement in Faust's original storyline, I simply don't see that happening anymore.
In fact, a few decrees aside, she's done basically fuck all with her position of authority. She's more or less a glorified ambassador, or a royal steward who's in the chain of command as a backup in an emergency.
If anything, I almost want to say that being a princess hinders Twilight more than helps. I mean, it didn't get her anything in the way of respect in Manehatten during that trip with Rarity, and aside from the times she gets to do her royal decrees or she gets ribbing about her status from one of the others, it's almost like everyone forgets she even IS a princess.