you clearly read ALL the Cullen fanfic then ... if you look for sex and romance fanfic you will find sex and romance fanfic, it's like you didn't even try to come up with a good point to make ...
As for the OP... why the hell not? He was a minor character in DA:O ... he still didn't have a big role in DAII albeit much bigger than in DA:O and it set up his whole spiel of quitting the Templars and Lyrium. He turned into a great character in DA:I.
Of course I went looking for stories with Cullen. BECAUSE HE WAS TORTURED. I found a sense of identification with the character because I have PTSD. It's something that doesn't disappear overnight. It sticks with you. You're always returning to that period in time when the abuse happened.
BW was always good to show broken characters. It's one of its strong points. And Cullen's fanbase seemed to be quite big. So I hoped to read some fiction that would portray how a person like that overcomes this huge problem. Fiction always helps to deal with trauma. And the possibilities for Cullen's character were huge.
Perhaps Greagoir would visit Cullen in Kinloch Hold? Perhaps Cullen would meet other templars who were also tortured? Pehaps he would start being cruel to the mages, as a form of compensation for his trauma? Or would he start taking more and more lyrium, as a form of escapism?
And then I tried to find ONE fanfiction that wasn't about Cullen being whored around, because that was the ONLY kind of story the fanbase were interested in reading and writing. I wanted something that spoke of his past, how he dealt with his PTSD, how it affected his work and his health. Something good, that actually had some content.
I found none. It's all sex, sex, sex, fetish, sex, sex.
That's how bestial the mentality surrounding his character is. Hence we return to the question: why is Cullen in all three games?
Answer: Just check the Cullen thread, AO3 and tumblr. And his VA's twitter.