Having played through both paths a few times, I agree with the OP. Helping the mages just makes far more sense. Cassandra and Leliana said it best. "There's a magister and a foreign power on our doorstep. That cannot be allowed to stand." I paraphrased that, but it's the gist of the response given to Cullen when he objects to going to Redcliffe.
Thinking that the Ferelden king or queen is going to deal with it doesn't make much sense, especially after you visit Redcliffe Village the first time and experience that time warp effect outside the gate. So, after you visit Alexius and return to Haven, you now know that there is a Tevinter magister - not just a Tevinter mage, a magister - who has taken over Redcliffe, a very important part of Ferelden, giving a hated foreign power a foothold in your own backyard. Not to mention a magister with the ability to time travel.
There is no reasonable leader anywhere that would not take swift and immediate action against that.
From a political standpoint, I could understand wanting to get the templars on your side. It does add credibility to the Inquisition and helps get the nobility behind you. But from purely an urgency and crisis management perspective, you'd almost have to deal with Alexius first.
Now, all the being said, from strictly a storytelling standpoint, the mage path is kind of stupid. Time travel? Really? If he had that ability then why didn't he just time travel back to the conclave and prevent the PC from interrupting the ritual? Problem solved. Corypheus takes over the world.
A hostile foreign power that is no threat to Haven. So the point is more one of how people will perceive the Inquisition. Hence, "the magister..." "Has outplayed us". And going along with the plan to be the bait and walk into the trap, it just feels like Alexius has outplayed you. The only way to make his play lose, is to avoid the trap and go for the templars.
Ferelden is not your own backyard. It's the crown's own backyard. Let them deal with it.
And who says the crown can't deal with it, or shouldn't? It's their mess, and they have the troops to clean it up, time magic or no time magic. And what can Alexius do with his time travel ability that he hasn't done already? That's the point. Any play he is going to make with time magic, has been done already. You can't stop it because it's already happened. So ignoring him and going after the templars is something he has already responded to, if he chose to respond to it. If he hasn't acted to counter you approaching the templars, then you win. If he has acted to it, then his trap at Redcliffe fails and he must come up with a new plan. A plan that you can take measures against. But as it turns out, Alexius fails to stop you if you go to the templars, either because he did not try, or anything he did try didn't work.
Swift and immediate action is too slow to combat time magic.
The only way to combat Alexius is with trickery. You must fool him into thinking that you will seek him out and walk into his trap. Then when the Ferelden crown shows up instead, that's when he must either use his time magic to change things again, or else flee. Either way, you defeat his trap. That's the only way to beat him without doing what he wants. Also don't forget that Dorian goes after Alexius himself if the Inquisition does not. So Dorian and Felix may have had something else in mind should the Inquisition refuse their primary idea.
The time magic required the massive outpouring of energy from the breach in order to fuel it. So the story was that Alexius could not travel back to before the breach occurred, and of course any point after the breach occurred would be too late, since the Anchor was set into the player character's hand before or at the moment of the breach. But yes, the mages arc is stupid.