I guess in that case the Inquisitor is already a big a power similar to a noble
Even better, really. An army at their command, vast political connections, land/estates that nobility are signing over to them, and the power to strip pretty much anyone of their good standing (thanks to Leliana and Josephine's maneuvering). The Inquisitor's just as, if not far more powerful and influential as many monarchs.
(Even if they don't have the power to can't get a servant to dust the spiderwebs or clean up the debris around their own castle
)
Combine that with the fact that the Inquisitor helps restore the Montilyet's good standing in Orlais, where the Inquisitor gains so much influence that the Empress or Emperor is in their debt. What noble merchant family would be insane enough to want to distance themselves from someone who can make them rich, at the least?
Hmm, maybe that's why Yvette was so excited to see the quiz? 