I wonder. Based on his own comments about working with a shrink and all, I wonder if it's more that he feels the weight of the coaches' lack of confidence in him and wants a fresh start. Who knows?
Well that wouldn't be a great sign. I'm a big believer in sports psychology as a tool to improve performance but if your issue is lost confidence because the coaches are mean to you or don't believe in you, then even some shrinks are going to tell you to get thicker skin as part of your improvement plan. They will focus on what you need to do to change the mind of that coach and you will methodically attack those problem areas. Part of that will be building up your own sources of unconditional confidence as well as working a process-oriented plan designed to incrementally achieve performance-oriented goals.
Michael Jordan is an oft-cited example of someone who used such a snub as motivation for his entire career. He even ranted about it at his HOF induction ceremony. It is potential fuel, which is precious to those who see it that way rather than a wound.
The exception to that might be if it's determined the coach is just unreasonably biased against you and has no real chance of changing his/her opinion, in which case removing that negative and restrictive influence would be warranted.
But just by inductive speculation I would be shocked if Bura's situation has been anything close to this severe. We can all see his play drop off for long periods and the same mistakes being made. We know they want him to do more and be less of a perimeter player. Is he stagnant because he doesn't understand what the coaches want? Does he believe in his mind he's making massive changes and the coaches don't see it that way?
Either way, if he wants out because he doesn't think the coaches believe in him, and they don't believe in him, none of the details matter and he should just be shipped out for the best possible return.