Bay is a lover too... I think their loving temperament, even with their hint of sass, is more important to to the breed than their style.
I agree. What you describe is also found in the best hunting dogs. It's that "I'm your best buddy, but let's go out and have some fun" attitude.
Some people hate the sight of Arabs doing dressage, but any breed can do it well. You just need to know the breed in order to judge whether the horse is doing well for that breed. Arabs have all the collected movements down pat, since they can just about roll themselves up in a ball.
I think it's the attitude that makes Arabs great sport horses. There may be no single thing they can do perfectly, but they can do most everything pretty well, and always have fun doing it. Just like with a dog, if you can convice an Arab that he's going to have fun, you'll have no trouble.