I think what therapy can help us to do is to learn different ways of dealing with a variety of stressors and situations and - more importantly - learn self-acceptance.
To me the term 'character defects' implies a lack of something that 'everyone else' has, but the reallity is that, by this definition, *everybody* has a 'character defect'. Which is where self-acceptance comes into it. We are all flawed human beings with our unique strengths, weaknesses and downfalls. No one of us has any more value than another (except perhaps for possession of financial worth!) We all have our challenges, our 'defects', our habits and traits that drive others crazy. AND we all have gifts to share with others - kindness, compassion, generosity, love, patience, tolerance or whatever... everyone has their strengths to share with others.
I definitely have areas of character that I consider to be 'flawed', but I don't think it is something that needs to be 'righted'. It is just a part or who I am - my uniqueness. To some others my flaws would be major ones, and too great to be accepted in an ongoing relationship of any kind. To others those same flaws are considered to be endearing quirks. What is seen as a flaw by one is not necessarily seen as a flaw by another.

So I don't believe that our innate character can be altered by therapy. As you say, we are who we are who we are. BUT, therapy can help us change our perception of those character traits that we dislike, and allow us to embrace our humanness, flaws and all.