You say the majority of mages are content with the Circle, then why does in every ending does the College of Enchanters form to rebel against it? These are the Inquisition's mages, the ones who helped fight Corypheus, not just Fiona and her flock at Redcliffe. In fact, if you recruit Fiona's mages, the College becomes the majority where as Vivienne's loyalists become only formidable because of muggle connections. So what proof is there that the Circle is even popular among the mages?
I also like to remind you that magic has saved the world more times than any muggle ever did. Solas saved the world by creating the Veil. Magic helped seal corypheus, the mark that the Inquisitor wields is magic. Even Andraste herself was suspected of utilizing magic to revolt against the magisters. Andraste wouldn't be able to speak to "Maker" spirits or fight against magisters at a time when templars and seekers didn't exist otherwise. And while yes, muggles outnumber mages, mages can still perform miraculous or horrifying feats as people mentioned. For example, a virulent werewolf curse, or a rampaging demon army, or just political scheming and turning the southern nations against each other. There's more than one way for a few mages to bring down the many and there's a reason why during the time of Arlathan, mages were considered gods and muggles the slaves.
The compromise is simple, give the free mages their own kingdom, a safe place for mages to live freely and not have to hide their nature. To learn magic unfettered with their own kind. Let the southern governments of Thedas have their own Templars under their control to utilize as defense against rogue mages and let the Chantry act as arbiter between the mages and the governments of nations. Let embassies of the College be around to provide magical services and admission to the College's kingdom where they can bring students there to learn their magic. Those admitted into the College are registered and exiled like the muggles want. If there is a magical crime, the Chantry should conduct investigations and even applications of justice, protecting both mages and common people impartially like the Inquisition once did (before it became complacent and corrupt) and use rhetoric to promote coexistence and true justice instead of punishing all mages to pacify the hysteria of muggles. When mages helped save the world, like when the mages protected Divine Beatrix III, the Chantry should hail them as heroes and respect magic instead of re-visioning the tale to only promote Cassandra's reputation. Disputes will be settled by the Exalted Council and the the mages should be represented in the Council. The Chantry will serve true justice and return to adhering to service to others, mages are no longer oppressed nor patronized, have a reason to control themselves, and the chantry could no longer use the fear of mages or templars to blackmail governments into submission like they did in Kirkwall. With autonomy, we free each other. For too long the Circle system has institutionalized profiteering oppression and hate. Is that really too much to ask to change all that especially when it's in everyone's interests?
What are muggles so afraid of that a free mage society could produce? If mages are really so dangerous as they say, the pressure of the Circle's oppression would unleash it eventually. Giving them a home instead of patronizing them with a Circle jail would give their lot more of a motivation to keep it all under the lid. If thedas is ever to know peace, they should not let the worse of them define them.
In first place, circles aren't popularity contest only security measure that exist in order protect world from magic that multiple times threatened world's safety and even more society. Second, most people by nature would chose improving own power and status so while college is certainly more attractive for mages it compromise safety of the world for a comfort of the few, what is ridiculous.
Well, that is fallacy. Sure, mages did help to solve those problems but funny part is that mages also caused those problems.
Why Solas had to destroy his world effectively leading to destruction of his culture? Answer is simple, cause of that was bunch of power hungry and self-destructive unstoppable mages who according to Solas would destroy world. Funny thing, Solas now tries to destroy current world because of nostalgia, what is good indicator that world safety shouldn't depend on whims the mage.
Why Corypheus was a threat in first place? Corypheus was a threat because he was a mage and darkswan (he caused blights even before he become darkspawn).If he wasn't a mage he wouldn't be much of the threat, unless he had a mage as subordinate but point stays.
Andraste rebellion the same, Tevinter was magocracy.
Nice utopia you got there, but this isn't even remotely how things work. In first place allowing mages to have nation is idiotic idea (Tevinter) and is practically begging them to take over, separating themselves from the little control chantry would have over them and exist as independent power just like Tevinter did. Second, corruption among mages would be tremendous and crimes would be covered up by mages that would be free to be self-serving, so basically mages would do as they please, occasionally throwing a mage under the bus for appearance sake just like Uldred did, at least until they would completely cut off from chantry supervision. Third, all above would come at expense of the people and world's safety, mages would start to conduct highly dangerous experiments and participate in dangerous activities with little force to stop them, that is even not touching matter of abominations that would be free to bring destruction upon world.
"What are muggles so afraid of that a free mage society could produce?"
Hmm, i don't know how about blights and other catastrophic events that mages caused? People have good reason to fear mages, they constantly demolish society with some horrific disasters.