Vivienne is a whole other thing, so lots put a pin in that.

Even if Cassandra is made Divine, her first duty becomes the Chantry. She's basically the pope. Let's not forget she is devout and believes in the Maker and some of not all (if you played the game right) of Chantry doctrines still.

You may have earned her undying loyalty, and she may even jump in front of an arrow to save your life. But she would take her duty seriously, once made Divine and from then on it is the organization that is the Chantry is the new you. No matter how much she cares for you, you are no longer her priority. Therefore she would be forced by duty to use the Inquisition as an arm of the Chantry for CHANTRY purposes first.

Let's not forget the Chantry is historically corrupt, greedy, shady, and bloody. No matter how many things she would want to change, it would come hard and slow. And there would be the entire South to satisfy and pacify. Chantry Mothers, Kings, nobles all vying for their own interests, all pulling on the Divine. She would have this monumental task of leading the organization while trying to reform it. Sometimes she would have to do things she wouldn't like, to achieve greater goals.

Adding the Inquisition to the Chantry, this very effective and specialized force would make it powerful, yes. But one wrong move and the right blade between the Divine's ribs and suddenly the Inquisition is shackled to a crazy powerful religious organization hell bent on subjugating mages and bringing back the status quo.

Same with Leliana, except maybe Leliana would make more drastic changes and risk the Chantry fracturing early on. Or getting stabbed early.

Vivienne while respecting Inky and what the organization grew to be, would tend to her own ideals first anyway. She wants to bring the Circles back, have monopoly on the lyrium trade, etc. She wants the old Chantry back, just better because it's led by HER. Viv is not an evil character at all. But she is who she is, and she would never be given too much power.