If I remember right- and I believe I do- it's because Vivienne's nominal relevance, a skilled politician with leadership over a bunch of mages, is never demonstrated. It's a tell, not show, situation.
Exactly. And there is hardly any "telling" whatsoever, either.
Vivienne had the potential to be a huge character, on a "most important NPC in the Inquisition, no contest" level of huge, yet nothing ever comes of it -- unless she manages to hijack the Divine election, which is hardly something that the players automatically consider desirable. Apart from that, neither her leadership of the loyalist mages nor her political connections exist in the game at all. (Granted, this may be partly because Bioware has generally not exactly handled political and subterfuge-related characters and stories remotely well.)
Plus, her dismissive and arrogant personality means that she better be doubly useful if I'm supposed to put up with her. She isn't. While I don't dislike her as much as I do some other characters, there just isn't anything about her that is appealing enough to warrant using her. Not her personality, not her (nonexistent) impact on the story, not her advice which while sensible basically amounts to no more than anyone with two working brain cells and/or a few moments in the presence of any noble or other power-grabbing politician can't figure out by themselves. (Same with Iron Bull's advice on leadership and troop morale, though that was presented in a more gratingly patronizing manner.)
I was also hoping for a character who would present a relatable and preferably "fair and balanced" pro-Circle view -- acknowledging the abuses and the need for change while also acknowledging the dangers of uncontrolled magic. As far as I remember, Vivienne doesn't do that, and in combination with her highly privileged position (hard-won and not merely inherited though it is) this makes her and thus a pro-Circle POV far too easy to dismiss. Especially for the parts of the playerbase that are already myopically and aggressively yelling "The Chantry and the templars and anything but absolute freedom and preferably dominance for mages is EVIL AND NEEDS TO DIE!!!!!!!!!!!!!!"
(Yet somehow Dorian's -- admittedly much less severe IMO -- flaws or Solas' desire to destroy the world don't seem to merit dismissing any pro-mage POVs. I guess it helps that players can use them for sex, which Vivienne has the sheer gall to refuse. Yes, sarcasm alert on the "sheer gall" bit there.)
Cassandra is the one who kind of provides a progressive pro-Circle stance, but she is not a mage so her words have less weight than the words of someone who'd actually live in that system.
Edit: Maybe I'm missing something by not using her more, going by what others here have said. It's just that there's no incentive for me to use her, and while I tend to be a hopeless completionist in some ways, I've learned not to force myself to accomodate characters I don't actually like while hoping it'll maybe, possible, somehow, pay off at some point.
So while I don't hate Vivienne and neither did she hate my Inquisitor (I actually finished the game with her approval pretty close to maximum), I do find her annoying and disappointing, and she really hasn't given me reason to change that impression.