Control of mages in the name of a god.
The thing is that that's not their only argument for doing so. The lesser argument, which I think would be insufficient on its own, is that mages can abuse their powers if they're not educated and monitored. The much better argument is that mages can go abomination, apparently whether or not they want to (though it can be done on purpose), and apparently whether or not they're been properly trained (to judge from the fact that the FE of Kirkwall apparently went abomination, and judging by the fact that she held back the demon so that the Templars could kill it and her she probably didn't want it to happen.) Mages don't unwillingly turn often, which is good because there probably wouldn't be a Thedas otherwise, but it can apparently happen, and judging by the Codex one Grand Cleric wrote to a Starkhaven noble what can happen at Redcliffe is apparently not an unprecedented example of what abominations can do. Even if it was down in the rules of the setting that magic cannot be used selfishly or immorally (and it is decidedly not) that would be enough danger to merit keeping mages separate from the general population to whatever extent is possible.
No, but it makes far more sense. If Alexius had the power to evict Teagan from Redcliffe, why would he tip his hand to Fiona before doing so and possibly get the mage rebellion and the arl's army both on the alert against him?
It's possible that he didn't want to go to the effort until he had Fiona in hand. That said, the fact that this is your argument leads me to suspect that Fiona didn't comment one way or the other on the order this happened in.
Is that the case? Because if she had been railroaded like this by Alexius, you'd think that she'd have said so when Anora/Alistair/Anora+Alistair were in Redcliffe side-eyeing her: if Alexius had made himself the only source of relief in evidence against an attack Fiona had thought was coming right then she might have been able to talk the Crown into showing her mercy. Come to think of it, that's actually a reason for Alexius to want her to sell herself to him of her own free will: this way, it's harder to mend the fence with Teagan's boss(es).