I'm going to paraphrase Hackett here to explain why it's the Inquisitor in charge and not Cassandra or Leilanna... "You can pay a solider to march, you can pay him to take a hill, but you can't make him believe." With Cassandra or Leilanna in charge, when they would walk in to recruit people would say "what gives you the authority to tell me what to do?" What are they supposed to say? "Because I'm a BAMF and I said so"? Where as the Inquisitor can jut walk up to a Fade breach, close it and say "That does. Now help me or let the demons take you."
But there is much more to the game than just the fade breach. You should read the graphic novels (The Silent Grove, Until we Sleep and Those Who Speak) as well as the books (Stolen Throne, The Calling, Asunder, and Masked Empire... especially Asunder and Masked Empire) for a better understanding of what we are walking into. You have the Dragon Cult, Mage/templar war, Orlais and all it's drama, Tevinter and the Qunari. All of these play a factor in what is happening in Thedas.
As far as attacking the Grey Wardens, we don't know if we are attacking or taking back a Grey Warden outpost. We don't know if there is a fade breach there or if red lyrium has taken control of the Wardens. This is all speculation based off a few seconds in a demo or trailer. Only playing the game will reveal what is actually going down.
So why some may want to simplify the game into... Step 1: Big Boom Step 2: Something Something Step 3: Profit/Romance. It really is just a disservice to the vast world that has been created. Please go get the books and read them. It will give perspective on everything that is happening all around Thedas. Heck even watch Dawn of the Seeker (an anime film with Cassandra) and Redemption (a webseries starring Tallis).
But back to the original poster's question, here is the story of the game as best I can tell.
The world of Thedas is already in epic upheaval. The mages and templars are at war, there is a crazed sect of Templars who take red lyrium. Orlais is in the middle of a civil war between Empress Celene and Duke Gaspard. Fereldan is on edge preparing for war with Orlais as Gaspard wants the province back. Tevinter and the Qunari are still at it. There is still the after effects of the Blight to contend with as well as darkspawn wandering about. We open with the leader of the Chantry and the leader of the mage rebellion coming to the Temple of the Sacred Ashes to discuss peace. During these talks someone or something sets off an explosion that kills everyone, but our Inquisitor. Who we are and why we were present at the talks has not been revealed. The veil is ripped however and demons start pouring out from the fade, we are pulled in. When we awake or what have you to be found by Cassandra, we discover that one we are the only survivor and two we can close fade tears. Cassandra takes us into custody, presumably for questioning that ends up proving that we didn't set off the explosion, but I have read that if we are a mage we might have indirectly contributed to the fade tear.
Our ability to seal the rifts is what puts us in charge of the Inquisition (speculation, but makes the most sense IMHO). An ancient backdoor organization created to help in times of severe trouble. It is not part of the Chantry nor does it answer to them though the Chantry was going to implement this Plan B if the peace talks failed. Our job is to restore order to Thedas. Close the fade rifts. Create an army to combat the demons. And find out who or what was responsible for the catastrophe in the first place and stop them. All the while having to deal with the plethora of issues that was already plaguing Thedas. We have to navigate the delicate balance of military might and political intrigue before everyone in Thedas is doomed.
Hopefully this helps original poster
Check out those books by the way, they will assist immensely me thinks.