@Jake's link: I'm not exactly certain that the content there - the writer's not really having a solid concept of the 'change destiny' spell is that big of a deal. The writers have admitted to letting the fine details slide before, and in-episode the effect was decently solid. The idea of the spell, clearly, is to give somepony a new path. The spell was kind of busted, so could only
swap destinies. Twilight's revelation was that destiny could only be changed with the aid of others, and so she had to get her friends to channel their magic along with hers.
The question of why she then became an alicorn is a bit trickier, but we know from Cadence's story that any sort of 'magical superevent' can create an alicorn, so it's possible that alicornism is just a side effect of the sheer amount of magic needed for the spell. It could also be a side effect of the fact that the channelers she used were the elements of harmony. Which raises the idea that somepony using the Change Destiny spell would have to piggyback on the destiny of the channeler, and so the result is kind of predetermined, and they'd have to find a pony who already sort of matches the destiny they want.
Anyways, the point is that while yes, Twilight becoming an alicorn is a
little arbitrary given the context, it's easy enough to come up with an explanation for and I don't think the vagueness has a huge effect on the episode.