I understand that to some people the mere open admission of faith makes one a fanatic or even a zealot, but that really isn't the case. Leliana is just faithful the way someone is faithful who believes they ought not hide their convictions. Her ability to listen to open criticism of her faith without blindly attacking the person making the criticism should tell you she is no zealot/fanatic, at least not in previous games.
What she is now? We don't yet know, but I'm not making any judgments based on how she behaved after just being released from torture. Don't any of you think you'd be a bit ... well, bitter and angry after something like that?
Also, why on earth do you think the devs would just go and let you bring down the Chantry in this game? The Chantry, in its own way, is an entity on par with any of the nations. Did they just let you go and dissolve Ferelden or Kirkwall if you decided you didn't like them at all? Basically, letting the player just destroy on of the major entities in the game would be to drastically remake large parts of the underlying world and lore. Yes, you make effect some major changes, but to allow you to knock one of the cornerstone pillars down is something I just don't see happening. I don't even see the ending of the Fade Breaches to be affecting any real end to the cosmology in terms of there being a need for a Veil although there may be some changes.