I would be interested in hearing your reasons, yes.
The short version is that at that moment Meredith was justifying an Annulment because the masses were afraid of the Mages, rather than the threat of the Circle itself. My overriding view of the Templars is that their guardianship over the mages is two ways: they protect the masses from the mages, but at the same time are to protect the mages from the fears of the masses. The same person who is the shield of the masses against the mages is also a sword to cut down mundanes who would try to kill mages for fear rather than any actual crime*. The Circle did not commit the crime, nor was it an immediate threat to the masses, and so it did not warrant an Annulment despite the corruption within it.
Put into practice, the Templars should have put the Circle into lock down with all the mages inside, fortified the Gallows, and cut down any mundanes who tried to mob the mages while weathering the fear-riots until the Chantry could send support and restore.
*If there's a scene or random encounter I feel was missing from DA2 and hope to see in DAI, it's a scene of Templars standing with swords drawn, backs to mages, between them and a lynch mob. It'd be an excellent point for a player character of reputation to arrive and resolve the situation violently or peacefully in various directions. (Calm the mob down, convince the Templars to not interfere, fight the mob alongside the Templars, fight the Templars and Mages with the mob.)
The longer version is that Meredith was calling an Annulment for her own interests about the Circle, rather than because of the Circle itself, and that the Annulment was convenient rather than necessary.
First and foremost, her public position. When she appeals to the masses (they will demand, and I will give it to them), she's completely disregarding any premise of justice and working from a position of self-interest of the Templars role in Kirkwall. Even if we discard greed for more power by winning approval, an insinuation raised is that Meredith and the Templars stand to lose a lot of power if they don't give the masses what they demand. All those Templar guards in the city? The Templar influence, recruits, the very premise of Kirkwall as a Templar stronghold? Those would be challenged, even threatened, if they don't execute the mages. This an extremely pragmatic, ammoral, self-interest argument for the Annulment of a Circle, but not one based on legitimacy or justice or even need.
It's an implicit argument for Templar interests, not Templar role and responsibilities, and I find it unmoving. I'm far from blind to the benefits of having power, but the Templars being so involved in Kirkwall politics was an overreach that distracted them from their mission. Yes, refusing to Annul the circle would have carried costs... but preserving those gains are not the purpose of the Templars. The Circles and Mages are. In the end, a system with insufficient justice and legitimacy to encourage buy in from its members is begging for failure and rejection. Meredith was placing political interests (which, while beneficial to the Templars, should not be their priority) over the interests of her charges (which are her priority). That is wrong on both pragmatic and moral grounds: morally because the Templars should be mission first, politics later, and pragmatically because the Circles need mage buy-in.
Secondly, I didn't see Annulment as a necessity. Not even in the sense of 'the costs of not doing so are bearable', but rather 'you can still do more rather than kill them.' In this point, the Annulment was being used as a convenience (tied to the above), not a last resort.
Proving I'm still not a bleeding heart despite the idealism hinted at the above, here's what I think a non-insane Meredith could have done short of Annulment, and could have gotten away with: do away with the balance of power and rights that allowed Orisino to obstruct here.
This isn't instead of what I wrote above, mind you, but rather in addition to. Call for a Circle lockdown, get all the mages into their rooms, barricade the Gallows, and then once a sufficient force of Templars is inside and out, have a nice, direct chat with Orisino before calling for a mage gathering and announcing that, instead of an Annulment, there is a state of emergency and the Templars will be conducting an unlimited investigation of the Tower and its inhabitants. The Circle system's rights and privelages are suspended for further notice, and martial law is in effect.
What would this mean in practice? Meredith does away with the balance of power and Orisino's ability to obstruct her. Do away with him as well if he objects: if he's smart, he'll do what he said at the steps of the Chantry and help her search the rooms. Which can be done any time without permission or warning. Leniency for transgressions, and obstructions, will likely be minimal: if Orisino's dirty laundry is found, he'd probably be the first to go. Blood magic, spreading through the city, is highly suspect, and even cuts on the common hand points could be enough. Tranquility could be meted out to newfound crimes, and past offenders who were spared by Orisino's interferance might find themselves in a new job or afterlife as the 'corruption' is rooted out. The Mages would likely be isolated, split from one another, and likely kept in their rooms for the immediate period.
Which, considering the fear and likely flames in the streets of Kirkwall, would be the better option of bad and worse. The mages lose rights, the grip tightens... but the balance of fear lets them live, and when the Chantry sends support to calm the streets it also turns attention to rectifying the Circle. This would hopefully entail the rollback of restrictions and reforms, but could also entail a more nuanced focus and investigation. For all that these threads focus on the sins of the Templars, few people have ever noted how badly the Circles act as police states. Spies, snitches, blackmail- there are a lot of ways the Templars could infiltrate the mage ranks to hunt for corruption.
I doubt the Chantry could outright remove Meredith at this point immediate post-crisis, or would particularly want to, but the Circle system would gradually reapply itself, and the grip loosens from outside influence and attention. The state of emergency ends, at least officially. The First Enchanter is restored, and his consent is needed for Tranquility. The basic mage rights return- maybe not as they once were, with Templars openly inspecting rooms and reading mail, but the room confinement ends and business starts to return. Mages can leave the tower on sanctioned business, at first with heavy escort and then, as the situation calms, with less. Templars are dominant, but with the recent event of Anders on the minds every mage knows they'll be considered guilty by the public by default: certainly suspicion of ties to Anders and the like would be thrown around freely, and Mages not being able to challenge it.
Not a pretty or nice sequence, but livable. Justifiable, in some respects, as part of a very real investigation into the mage-side of problems in the Circle, even if it just accentuates the Templar issues for the immediate period. Arguably preferable, for those who didn't prefer being Anders' sacrifices. It also offers a way to avoid the immediate war, and extends that low chance for compromise and reform: in such a context, the Divine's efforts for Circle reform may get more traction without going off the wheels like Asunder.
Mind you, that's the middle case scenario. Worst case is that the revolutionists attempt a rebellion against the martial law and intrusive investigations, which sparks its own Annulment. Which is bad, but happens under a different context and so might not lead to a wider war if the narrative goes from 'the Templars Annuled a Circle for the crimes of an Apostate' to 'the Templars Annuled a Circle that resisted investigation after mage terrorism.' Which still might help avoid the immediate Chantry civil war.
Best case is that the martial law investigations do find evidence of corruption, and purge the bad actors within the Circle including Orisino, while Meredith is removed by the Chantry's reinforcements and/or post-crisis Seeker investigation of the crisis (which could find Meredith's contributions and Templar abuses in the leadup) and Meredith's suspension of the Circle rights (which might or might not be punished outright, but would certainly be worrying). On top of the global reform efforts by the Divine, local reforms for Kirkwall in the short term could be pursued by a change of leadership that such a crisis could prompt.
In summary, even if Meredith stops short of Annulment and executes a paranoid police state of the Circle, she can lock down any actual mage threat in the Circles without Annulment (the period of Kirkwall chaos and Circle martial law) while the events of climax would give an impetus to get other parts of the system working and responding to Kirkwall. The only mage threat this wouldn't directly address was rogue mages in Kirkwall outside of the Circle- but these wouldn't be addressed by an Annulment anyway.
Meredith could have done this, and could have been a lot more palatable and justified in investigating for ties to Anders (his old Circle contacts, if they remain) and blood magic (which exist) rather than executions.
Or at least could have, if Meredith wasn't uncompromisingly insane by the Lyrium idol. Which she is. Which is why she chose Annulment, and I chose to stand against her.