The controversy, in itself, will only be ended when this team has a quarterback that takes the reigns and leaves no doubt as to whom should be the starter.
The situation with AJ is a bit different though. He's a young quarterback that has shown the potential to be an above average starter in terms of the talent that he has. He has also shown that he has some things that he needs to work though, and to do so, he needs to play. The season he had last year would have wrecked the psyche of many young quarterbacks, and I believe that letting the doubt in that he may not be the guy to go with in the long run could do more harm than good.
This is the toughest position to evaluate in football. There appears to be a thin line between giving up too early on a young quarterback and sticking with him for too long. The patience Seattle exhibited with Matt Hasselbeck paid off in the end, and San Diego had all but given up on Drew Brees. Conversely, you have situations like Miami sticking with Jay Fiedler despite the obvious fact that he couldn't do the job.