I may be mistaken, but we have yet to see a non mage possessed by a demon that didn't involve the veil being weakened. On the other hand, between the games and books we have seen a plethora of mages get possessed at any number of times. Heck in Last Flight they talk about the commonality of Grey Warden Mages to let themselves be possessed right before they are overrun by the horde of darkspawn in an effort to take as many with them as they can. In fact we see a warden become an abomination while riding on his/her griffon.
Whats more, and what makes the true nature of the gun analogy is that if any of those non magic beings or objects become possessed, while yes they do pose a certain level of danger, they are not the world destroying danger that is an Abomination.
Against a normal possessed human or tree or what have you, a normal person has some chance at fighting back, against an abomination on the loose, they don't. We haven't heard any stories of Grey Bark the flesh devouring rampaging tree killing hundreds, we have multiple accounts of abominations doing just that.
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.