Well Alistair sorta sealed his own fate by acting the way he did in the Landsmeet, really. Bran did not plan on getting rid of him beforehand, if it makes you feel any better, he was fine with letting him stay in the Grey Wardens – because he genuinely thinks Alistair is more suited to this life and it’s a life he wants and is good at, and he’s sure he’d make a fine leader once he grows up a little bit and becomes more confident. And that would happen when Bran is not there anymore to fill in the role that was supposed to be his.
But by claiming the crown just to get his revenge – on a whim – by throwing a temper tantrum in the middle of a crucial and highly political meeting, he just proves he’s a liability. If he had agreed to remain within the Wardens, Bran would have had no objection. Leaving them, and thus becoming unpredictable, is not an option the new rulers can afford to take. As I said, Alistair is the only true threat to either Anora or Bran’s rule, and they’re both too politically savvy to let him go. It would be living with a sword of Damocles hanging over your head – they have no guarantee Alistair would remain true to his word and not attempt sthg once out of reach, and ally himself with their opponents. And even if Alistair does none of those things, plots can still be carried out in his name – we have one in canon, so it’s not even speculation at this point. He is dangerous.
Because whatever Alistair says, it’s pure revenge and hatred that drives him here. He wants to kill Loghain because he blames him for the death of his father figure. For Bran, being in the Wardens is already a punishment, and making Loghain one of them is a sentence in its own. Plus Bran knows how Loghain is important to Ferelden’s history and identity. He is the hero of River Dane, after all. Making him a Warden neutralizes him politically and makes him answerable to a higher authority. Of course Alistair doesn’t share this point of view at all, since for him being a Warden is a calling and there is no higher honor than to serve among them *cue Bran laughing in the distance* So fondamentally, they’re just bound to misunderstand each another.
And I know Alistair doesn’t want the throne to begin with. I’m not the one making the choice here. I can’t see Bran letting him walk away when he knows what he knows about Alistair’s character. And Anora being pragmatic as hell… It’s a similar situation to Mary Ist and Jane Grey, or Elizabeth Ist and Mary Stuart. It’s nothing personal.
I’ve written more about this here, if you’re in need of meta to understand this decision.