Because their chances were already pretty good. You can do desperate things to win a war, but you want to be... actually desperate first.
And the desperate things should actually advance your position.
In selling herself and the magi to Tevinter, Fiona increased the war potential of the mages by... a few more mages, mainly whatever retinue Alexius brought with him. This came at the cost of the political, military, and diplomatic support of Ferelden, which was lost when the Arl and all the Arl's forces who left with him departed.
Even in the face of a Templar attack, this is a Bad Deal. The unique and significant ability of the Templars is their anti-magical abilities. The best defense against them is mundane military power- or blood magic. Alexius's benefits of the former are negligable- Tevinter has neither the forces nor the logistics nor the interest nor the time to move an army to Redcliffe. And if Fiona is counting on Tevinter to win the battle with blood magic, then the question of 'where is the blood coming from' becomes highly important. Certainly the Tevinters aren't going to kill themselves, and presumably they aren't going to kill their new mage-slaves, so betting on a blood magic defense would be Fiona betting on the blood-sacrifice of the villagers of Redcliffe- a crime compounding her betrayal of Ferelden's prior aid.
Fiona or Alexius might claim that Alexius's coup won them the castle for security, but this is a losing proposition. There has never been any credible threat or indication that the Arl of Redcliffe was going to put up the drawbridges and let templars butcher the town and mages. Redcliffe Castle, with the backing of Ferelden, was a safe haven that could reliably be expected to hold off a Templar seige until the Royal Ferelden Army could bring in forces to break the siege. Kicking out the Arl (or, more accurately, not intervening as he was deposed) turned Redcliffe Castle from a safe-haven into a death trap- unlike the Templars, the Kingdom of Ferelden could be reasonably expected to lay seige to reclaim their castle. No other visible power could have or would have had reason to intervene, and the only reason Redcliffe didn't fall was because the Venatori kick off the apocalypse- a meta-argument that damns the mages far more than defends them if raised.
As soon as Alexius launched his coup of the castle, Redcliffe was a trap for the mages that needed to be escaped as soon as possible. It was a self-defeating move that should have immediately raised red flags amongst the mages- the only rational for ousting the arl (to take over the castle) would instead only ostracize, alienate, and give them more enemies who, unlike the Templars, actually would have a force that could lay seige to the castle.