We also have seen how organizations can hold puppet governments. Meredith and company had a puppet in Viscount Dumar but, even then, he had power. Not MUCH power but power. Also, when they tried to rule directly, the Templars started to lose their power.
Keeping up appearances is important.
True, Kirkwall was another example of a failed state because the legitimate forces of the city-state were actually weaker than the Templar garrison.
I know that a lot of people see DA2 as a story of Mages and Templars, but I saw it more as a tale of the separation of church and state, and the nature of the state itself.
The Templars held a lot of power after they deposed the legitimate Viscount and put a puppet-ruler in his place. That Viscount had tried to kick out the Templars after they pressured him to favour Orlesian interests. Talk about church interference in wordly matters. Act 2 is a story of how the puppet-ruler tries to solve the situation (and fails), and Act 3 of what happens when not even appearances of legitimacy are kept. Aveline complains that the Templars put obstacles to the Kirkwall guards, and nobles complain about Meredith's rule and start looking at Hawke as a good candidate to oppose Meredith.
It also explains why pro-Templar Hawke was attacked by Meredith in the end. Because they were the only figure left with enough power to oppose the Templars. I'm not saying that it was lust of power what motivated Meredith, mind you. Red lyrium fueled her paranoia. Paranoia against mages, evidently, but paranoia against nobles too. We know of her past trauma with her sister, but let's not forget that it was a mundane, not a mage, who had her predecessor, poor Knight-Commander Guylan, hung. Hawke was likely a threat in her eyes, a possible Viscount Perrin 2.0.
The ideal canon is unhardened Alistair, Chancellor Cousland with Teyrn title, Viscount Hawke (which might happen if you side with Mages in both), and both of them serving (with?) the Inquisitor.
You could make a decent ruling Triumvirate from those three.
But Viscount Hawke only happens in the Templar ending, and only for a year or so. By the time DA:I starts, there's no Viscount Hawke anymore.