Lawful vs moral debates are like trainwrecks to me.
I can't look away.
But atleast they don't make me bash my head like religious and political debates.
Same here.
Anywho, my take on it.
Whether you morally agree with the Chantry's authority or not, they have been given political power throughout Southern Thedas in many nations, and the templars have been given authority to deal with mages so long as they were part of the Chantry and the Seekers had authority over the Templars so long as they were part of the Chantry and the empires and kingdoms of Thedas respected that authority.
When the Templars and Seekers broke away from the Chantry, they in effect lost what authority they had. Cassandra, as of DA2, had not left the Chantry and was acting with Divine Justinia's approval, thus retained her authority within the Chantry hierarchy, and thus was respected as an authority by Kirkwall and the kingdoms of Thedas.
After the explosion at the Conclave, the Chantry was leaderless, the templars were rogue, the mages were rogue and an Inquisition was on the rise.
The Chantry retained its power because of the united faith of Southern Thedas, and the Inquisition gained power either through marshall might, ferreting out secrets or through political maneuvering.
Essentially, the beginning of Inquisition until the end wasn't about lawful good or moral good. It was a "might makes right" situation where the Inquisition became a power in the world because it established itself as something that was solving the world's problems when no one else was, or could.
We couldn't supplant the Chantry, they are too widespread and popular, but we could affect its direction with the choice of a new divine, and we could influence the direction of Thedas in many, many ways.