Actually, some of your questions have pretty good answers.
"It is as logical that that was her next step as it was logical that it was any of the other main sixs next step."
No, because Twilight was the only one of them under the explicit training and guidance of Celestia. You'll recall from the Wonderbolt Academy episode that it's mentioned that Celestia has Twilight working on some sort of new spell. Twilight is also the only one "tested" by Celestia. While the rest of the Mane 6 do write letters to Celestia, Twilight is her primary focus. The Elements of Harmony parallel this. The elements are powered by all of them, but the power is exercised and manifested through Twilight. This is emphasized multiple times. At the beginning of Season 1, Twilight's friends are positioned around her, with Twilight in the middle with a large crown. This quote makes this more evident:
"You see, Nightmare Moon, when those Elements are ignited by the... the spark, that resides in the heart of us all, it creates the sixth element: the element of... magic!"
Twilight's power and position is entirely dependent on her strong relationship with her friends. She is the element of magic, and since friendship is magic, it makes sense that Twilight is the central character. She's a manifestation of the magic of friendship. Thus, her status is indicative of the power of the elements of harmony and the strength of her friendships. In a way, all of the Mane 6 is the alicorn princess. A possible future episode might involve a disruption in her friendship (like what happened at the beginning of Season 2), causing her alicorn status to become lessened.
"It isn't a matter of her getting closer to something or being better at something she had trained at, it is a radical and fundamental change that came out of nowhere."
Remember, an alicorn is still arguably a "unicorn." An alicorn possesses characteristics of all three races. Remember, she is studying under Celestia for a reason, so she is in fact "getting closer" to something. Lauren Faust envisioned her becoming Celestia's successor. An alicorn is a balance of all three races AND uniquely magical, which makes it a good fit for such a position.
"Not only had it no build up storywise"
While it is certainly arguable that her transformation was rushed and premature story wise, it's not possible to argue that there was no build up at all. The Elements of Harmony are the biggest buildup, as it establishes a framework under which her ascension makes logical sense. Additionally, every single episode resulted in her learning more about friendship. Friendship is magic, so massive amounts of friendship (and knowledge of) --> massive amounts of magic, to the point where she was able to write her own novel spell which activated the transformation process. There is deep magic in the Elements of Harmony, and it has been shown time and time again that they are powered solely by friendship. Twilight's spell was the ultimate friendship spell, so it makes sense that it would activate the Elements of Harmony in a unique way (they are after all literally the things that zapped her).