Sacred Haven of Debauchery

But the rulers of Tevinter do not become possessed, at least not on a massive scale. Doesn't this suggest that mages can also monitor the behavior of their peers?

Not on a massive scale. But they are not immune. As for controlling mages, let me remind you about Uldred; he successfully concealed himself for a while, and then a good half of the circle became possessed.

And she also subdues mages who have undergone trials, which is forbidden in all other Circles.

I think this is acceptable. Grace also underwent trials, but she practiced blood magic. But, despite her obviously evil alignment, she was not subdued. Therefore, they only subdued those who were obviously involved in dark deeds, or it was the "templars' own initiative." Have you forgotten about Ulrich and his brethren?