Well I don't know about "possessed", but a plenty of non-mages have gotten influenced by demons (the Templar during the Broken Circle quest, the woman who was responsible for the Vael murders) - but true, most of the time this happends when the demon is already outside the Veil. And yes, abominations are deadlier than regular mages or possessed corpses, but we do have accounts of Sylvans wrecking stuff - not quite Isengard-level of destruction, but they seemed to do pretty decent damage in The Masked Empire. Point being, magic and demons are dangerous, but it's not just the mages who are the problem, and isolating the problem to a selected group of people in a world which is literally full of magic is putting bliners on the general populance and telling them the mages are suffering from the Maker's judgement since the Tevinter magisters were the ones who killed Andraste. It's giving a false sense of security.
But anyway, even if we dismiss that point, the question remains - how do we keep mages from turning into abominations? By subjecting them to the Harrowing, keeping them in isolation and treating them like misbehaving sinners who don't deserve freedom or agency? Or by giving them a reason to resist, not just the tools and the means? All other things being equal, isn't a mage who has a reason to resist possession (societal connections, family etc.) more likely to do so than a mage who's living under constant fear and judgement?
The the Circles operated by creating an isolated populance with little to no social contacts, then topped that off with a bit of religious dogma made to make them feel guilty about who they were and what they could do, and made this the reason they were denied freedom and agency. That gave the mages two possibilities: to either internalise a negative self-image or to reject it, so we have people with powerful abilities who either 1) hate themselves to some degree or level, or 2) hate the system that wants them to internalise a negative self-image. Of course there are also individuals such as Wynne who accept their captivity and agree with the Chantry logic, but I'd argue that even she carries some psychological baggage regarding her status as a mage (or has isolated that part of herself - ie. "I'm not like those other mages").
But all in all, I'd actually argue that from a psychological point of view the Circle is unwittingly manufacturing potential possession-victims in stead of helping them to use their gifts/talents safely. That, and putting the mundane population in danger by making the mages the go-to scapegoats when it comes to demons and demonic influences in stead of recognizing and adressing the real problems.
The Chantry dogma doesn't make mages have a negative self image of themselves. As Justinia herself said, magic is a gift from the maker.
Now, the idiotic interpretation of some misconstrue this? Sure. But you have that in everything. You have mages who misconstrue things for their own benefit and interpretation, as you have with wardens and others.
Also, I wouldn't make the argument that Thedas is teaming with magic. Gaider and company have been very consistent on the point that Thedas is a low magic world compared to most other gaming worlds.
I will admit that the hard line stance of the templars that we currently have seen to predominant the templar ranks causes problems and issues, but I do not think that is an intrinsic failing of the circle systems. The circles have been around over 900 years. We haven't gotten specific stats, but I believe estimates range from 20-30 circles( I found this number high, but it is based off a comment made by Cameron Lee) not counting tevinter, and I believe we have figure up from the WoT that there have been 19 ROA in the 700 years it has existed(possibly 20 depending on how you handle the circle in DAO).
So if you say 20 ROA in 20 circles over 700 years...thats not too bad a return on investment for security. Yes, I will argue the templars of late have been harsh, but the point that is always missed is the mages are not without blame to a degree for the deterioration of the situation.
The system works as it has shown. The ancient records of hedge wizards going crazy, chasind possession, the very need for the inquisition in the first place to both protect and police mages indicates a need for it.
Also, it isn't like a bunch of mage hating orlesians invented the circles, they took the idea from Tevinter who first created the circle systems and the harrowing I believe.
The system works. It and the individuals involved needed reforming yes. Notice I said the individuals, mages and templars. There are mages that are just as much uncompromising hard liners as there are templars. Adrian and Orsino to me are just as guilty as Lambert and Meredith.
However, the answer isn't to let mages live their lives and run around willy nilly living wherever they wish without oversight or training.