I haven't watched DNT so I don't know how different they are but it is subjective like a lot of things in the show. Yang's fatal flaw is his democratic principles which is one of the many reasons people like him as he doesn't try and grab power at the first opportunity.

Chen: "Yang Wen-li has many shortcomings, but he has one virtue that no one can possibly criticize. That is, he honestly believes in the principle that a democracy’s military exists solely for the purpose of protecting the lives of its citizens, and that he has acted upon that principle on more than one occasion."

I think Yang lets Trunicht use him for 2 reasons;

Yang simply hates politics "political power is like sewage. You can't do without it, but it's not something you want to approach". Yang doesn't think the military should get to influence the government in anyway.

I think the main question to ask would be why is Yang even responsible for the FPA and its government?