Lalala alicorns and characterization and... there's not really any concise way to describe this spoiler, is there? Anyway, a couple of points that occur to me.
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I'd like to point out, first, that this is a world with magic. Magic, further, that explicitly can effect physical changes, specifically granting new abilities.
That being the case, then, I'm not aware of any particular reason to suppose that Celestia abdicating in favor of Twilight, and Twilight becoming an alicorn princess, is necessarily different than, say, Edward VIII abdicating in favor of his brother Albert, who then became King George VI. Obviously there'd be some kind of magical ceremony, but given this was established as a "magical land" in the very first line of the first episode I'd be highly disappointed if any legitimate transfer of power didn't have a magical ceremony.
Your position on the desirability of characters changing confuses me. The status quo works, therefore change is to be avoided? One unicorn is known to dream of royalty, and there's reason to believe others do, therefore one who's shown no sign of it isn't allowed to be royal?
Now, certainly, if Rarity were to become Princess Out Of Nowhere, that would be jarring and probably a bad sign. But I can see the edges of how such a thing might be set up in such a way that it wouldn't be. It'd require character development on her part, and considerably more interaction with Celestia, but it could happen. How much more plausible and viable, then, is it for Twilight, who not only hasn't shown interest in becoming royal for the sake of becoming royal, but also already has connections at that level?
I feel like I got off track there, but I'm not sure how or where. The point I think I was trying to make was, good things happen to people. And that's allowed to be the case even if they're good people.