The idea behind the Circle is not to punish person X; it is to remove them.
That might sound harsh, but sometimes physical separation truly is the best way to settle conflicts. Domestic violence is an example of this. There are also many historical examples, where new nations were formed to separate warring factions (e.g. -- India and Pakistan).
In cases of domestic violence, the abuser is guilty of... abuse. Yes, separating a violent abuser--a criminal--from his victim is a good thing. Yes, care must be taken, because that's when the abuser is most likely to kill his victim.
Most mages are not guilty of anything. They're stuck in Circles anyhow.
Also, the example of India & Pakistan is--in my opinion--a prime example of how separation can go wrong. Thousands of people died in the process of separating India and Pakistan--the forced migrations alone were devastating.
Also... how well has that worked out again? Because India and Pakistan have been on the brink of war ever since the land was partitioned. They have nukes pointed at one another. Pakistan has nukes because of India. Pakistan having nukes is a danger to everyone.
If you ask me, Pakistan & India is a disaster. The negative effects have snowballed--as they always do.
It is understandable why the Chantry may feel like separation is the best solution.
Ignorance, fear-mongering, and punishing a minority faction in order to make the majority faction more comfortable are, indeed, UNDERSTANDABLE. Doesn't have anything to do with whether or not it's right. (It's not.)
Sure, people may fight all the time, but magic makes these potential fights a lot messier. When magic is used, innocent bystanders are at a higher risk of being harmed than fights using conventional weapons. Doubly so if the lack of a Circle results in a lack of proper training for the mage. Suddenly you have more involved parties, and the family or friends of the victims may enter the mix seeking retribution. Also, in a panic situation, mages run high risk of possession. Suddenly the death-toll shoots up exponentially (to the tune of 50+ victims).
And here we get to the usual arguments in favor of Circles, which have been debated ad nauseum. Sacrifice the few for the good of the many. And, yep, it's possible this would result in marginally less death and destruction (though if you balanced the lives saved through containment against the lives that might be saved if mages were allowed to live freely & use their skills for good, I suspect the balance would tip in the other direction.)
Now, more panic ensues, and the presence of magic leads to mages getting the blame (even if they were never the aggressors) and becoming the target of more violence.
"I'm doing this to you for your own good!" -- Vomit.
The Circle seeks to avoid this. In theory...
Theory is nice, but theory must be tested by results. The results have disproven the theory. So. Time for a new theory.