Warden is recruited because Duncan saw potential in them to become a leader, not a military general. You are leader of a small strike team, your goal is to put Archedemon down, not to become Alexander or Bonaparte. You need charisma and strong personality to unite different fractions, but you don't command allies army.
And you don't have time to train someone. The war is upon us.
I'm sorry, I can't believe that Orlais, a country constantly in war, somehow doesn't have any generals. Did Celine just destroyed her own military personnel, or something?
I also don't like how pro-templar Hawke (what was the point of that character existing, again?) and Aveline are reduced to nothing to make Cullen look good.
OMG. Good points ! Whatever happened to military personnel in Ferelden, Orlais (the two nations we will be going to), Aveline Vallen (who has more experience in being a leader than Cullen) and pro-Templar Hawke ?
All these people..who are way more qualified...swept under the proverbial bus for Cullen...
Talk about being a revisionist...
Yeah, this is because Cullen was carefully picked and selected to be a member of the team. It doesn't have anything to do with the Cullenites and the 1900+ pages about how good he looks. 
The Inquisition is an organization whose purpose is to, essentially cancel the apocalypse in Thedas. You do that by having rational, logical and capable people on the team.
I would be very happy and very willing to have Cullen on the Inquisition team and being a military adviser if there is a rational and logical reason to do so.
Problem is, there isn't any.
He is not the best templar out there. He is good but there are better ones out there like Gregoir and Evangeline.
He is being massively retconned both in Dragon Age 2 and Dragon Age Origins.
People who are far more capable and far more suited to the role of the adviser exist and they are all being thrown under the proverbial bus to make way for him.