There's nothing fast about it, mages have been in circles for centuries, might as well use the revolution for something.
Let me play devil's advocate.
I'm a farmer taking my cart to the town market, cool as you please, to sell my goods in a stall or something. Whistling a tune. As far as I know, the day is perfectly fine, my son was taken to the Circle by templars, la dee dah, I tried hiding him but accidental magic gave him away in the end. While in the market, I hear from a town crier that the entire circle has been liberated and all the mages were now free. Now most people in the market suddenly start panicking because they have centuries of religious dogma against mages vs a philosophical abstract (and one that I strongly support personally) that mages should have their freedom.
Many of those mages come to the town I'm in, and the townspeople are now expecting abominations and blood mages because for centuries that is what they've been taught to expect from any apostate or mage who isn't part of a circle, especially since the codex makes it clear that the templars and the chantry deliberately blurred the line between the two terms.
Now, me as a father of a mage may be happy, but the average person? How do you think they would treat the mages of a nearby circle where all the mages are now released, most of them are simply visiting to find the families that they were torn from?
The system itself is in desperate need of reform, probably needs to be abolished and set up anew. The old Circle system cannot be restored, there's too much bad blood on all sides, but it may be possible for it to be renewed, and that'll take trust and faith in each other from various sides.
But it's important to also recognize that the conflict goes far beyond merely oppressive templars or insane mages making bad names for both sides. You'd also have to deal with the cultural view on mages, and that cuts right to the heart of the Chantry's teachings, something that has been in place for centuries. The average person wold be driven into a chaotic mindset because their daily lives don't center around mages, keeping an ear to the ground and sensing the change. It would be abrupt, life-changing, and possibly quite violent, whether from the mage criminals who have a chip on their shoulder at their own injustice to the fearful mobs of mundanes who, even in current lore, gather and kill children as they're discovered to be mages for a bad crop, a still-birth or whatever.
It is a change that is going to be quite abrupt, and likely violent, and has very little to do with the Circle system and how mages are treated within it, and nearly everything to do with how much they're feared and how much they're preached against outside the Circles themselves.