I know this is an old thread, and I'm probably bringing up a very old argument, but I think everyone in most Wesley Crusher arguments keeps forgetting the ultimate and most important stage in Wesley's life: meeting the Traveller. The Traveller told Picard that Wesley was somebody like him, who would ultimately one day be capable of abilities like his way. Well, he implied so at least. And so isn't it obvious that the reason why Picard let Wesley do more around the ship than other crew members was because he knew that Wesley would someday have abilities far beyond them all, and he needed the chances to grow himself.
And later, when he leaves with the Traveller and leaves Starfleet, he makes that decision himself despite the fact that he will have to leave Starfleet and possibly this dimension to continue his growing, the final show that he's matured.
Just wanted to add this to the conversation.