Alright, I'm getting sick of reading this. I'm not even a fan of the guy, but the sheer amount of people repeating this demands a counter. I'm going to explain why Cullen was the only logical person to take command of the Inquisitions military forces, point by point.
So from the very beginning, the General of the Inquisition basically has to be either from the Grey Wardens or the Chantry. Why you ask? Because the Inquisition is trying to operate in both Ferelden/The Marches and Orlais, countries which have a long and incredibly strong mutual hatred for each other. Sure, Loghain or Gaspard have more than enough experience under their belt, but there's no way in hell they would be able to get near the other country's border with an army. To a lesser extent, the same would be true of a Nevarran general. He has to be from an international organization that is accepted in all of Southern Thedas, and that's a pretty short list: The Grey Wardens, and the Chantry.
So of those two, who are some likely candidates? Of the Wardens Loghain is dead in most playthroughs, and even so, Orlais would not accept him. Alistair and all the Awakenings companions are possibly dead, and I think only Nathaniel would really cut it as commander. Who does that leave us with? Stroud? That's not even getting into whether the Grey Wardens are compromised, though signs definitely point to "yes" on that count.
What about from the Chantry? Right off the bat, you'll notice the distinct lack of established Templar characters. We've got Greagoir, who is probably fairly experienced, but is getting on in years by now, and has other duties. And then there's...Cullen. A known moderate, with a likable personality, friendly disposition, and extensive combat experience. And when I say extensive, I mean it. Here, let's count:
- Survived Uldred's torture when no one else did, showing extraordinary mental strength and perseverance, even if it took it's toll on him.
- Participated in the Battle of Denerim, fighting with the Templars and/or Mages to fight back the Darkspawn. He survived, and his coalition won the battle.
- Helped command the Kirkwall Templars, a fairly large military order, for 10 years. Especially notable because of the sheer amount of crap happening in and around Kirkwall.
- Helped Command the Templars during the Qunari Invasion of Kirkwall. With Meredith personally busy trying to rescue the Viscount, it's likely Cullen had to lead the rest of the Templar forces in defending the city. He survived this battle, and his side stood victorious at the end.
- In the Kirkwall Rebellion, Cullen and his Templars stood against apostates, maleficars, and demons in claustrophobic urban combat. Even with...whatever the hell happened with Meredith, the Templars were in possession of the field at the end. They indisputably won that battle, even if their casualties were high.
You'll notice that Cullen's record includes basically every major battle that has happened so far in the Dragon Age, and his victory rate is 100%. Coincidentally the same as his survival rate in people's playthroughs. Coupled with his inexplicable but extremely passionate fan base, it would seem Cullen would be the ideal candidate for General of the Inquisition.
"Now hold up," you may say "why don't they just create a brand new character to be General, like they did with Josephine?" Well, that idea has a whole host of problems with it. They would still have to be either a Warden or a Templar, due to the above mentioned problems. Most Wardens and Templars don't really have a lot of military experience. That doesn't mean they aren't skilled or dangerous, because they are, but most Wardens and Templars fight in small groups, probably less than a dozen. The only exceptions are the aforementioned battles, at least that I know of. In addition, their motives are likely to be suspect. Why would a Warden, whose supposed to be down below fighting Darkspawn, suddenly volunteer to command the Inquisition's army? And keeping in mind all the weird crap going down with the Wardens, why would anyone give him that army? As for the Templars, enough people on the board's are griping about "being surrounded by the Chantry", even though neither Leliana or Cullen really have a hardline stance. Why would any elf or mage Inquisitor trust a brand new Templar character?
A new character would basically have to be Cullen: a Templar who survived the two battles in Kirkwall with moderate views and a friendly demeanor. And at that point, why wouldn't you just go with Cullen in the first place? What possible reason would you have to use a suspiciously similar substitute over the genuine article? I suspect it mostly boils down too "Because I don't like Cullen!"
To which I would ask, do you think you would like the new guy any better?