Treblaine said:
Like Wizzy said right after you, the Trekverse is pretty much a collection of unmitigated Mary Sues. Of them all, however, Kirk and Crusher take the cake. As to WHY this universe is fraught with too-perfect gentlemen or the occasional idealistic hard-lining leading woman (e.g. Janeway), it's largely because Gene Roddenberry was a secular humanist.
He was firm in his belief that the far-flung future would fix absolutely EVERYTHING on Humanity's overall scale, while our current problems would remain to be found on a bigger, pan-galactic spectrum. The Vulcans are the British, the Klingons are the Japanese, the Borg fit right in with the early nineties' lasting Cold War fixations. Voyager's Doctor likes opera when he could've liked Bruce Springsteen or Alice Cooper, because opera is "high-brow" and intellectual, at least according to the popular consensus. Tom Paris had a thing for retro-futurism because the fifties' Pulp serials were a direct influence on Roddenberry and had their own brand of stubborn naiveté. Star Trek is a universe where you can have your Flash Gordon fantasy cake and yet avoid dragging your crew into anything that's so messy as to underline our less-than-noble leanings. Everything's put in place so Humanity comes out on top.
Remember; we've been elevated by the Vulcans, and by the time Voyager rolls around, we've learned to balance our emotions and ideals so perfectly that planetary war is a thing of the past. The only thing that's left of it is a very romanticized vision of the way - WWII as seen through Holodeck simulations, where the Americans are *very* American and the Nazis wring their hands, buff their phony accents are are relegated to your average boogeymen.
If this is the norm in that universe, then things that disrupt that norm become Sues. Crusher's a Sue because there's no way in Hell, outside of sheer nepotism, that a kid his age would've ended up serving on the Enterprise. Yes, he's a genius, but Vulcans tend to be depicted as dime-store geniuses, too. You don't see them enrolling their kids into the Federation. Crusher's the Impossibly Privileged White Kid, and yes, that might be a form of intentional parody of some fans. Considering how honestly loathed Wil Wheaton's character was, I kind of doubt it was. I'm still of the mind that he was a rather sincere concept that had gone awry.
I think Wesley Crusher was meant to be another facet of the awesome-tastic and utterly infallible Federation of Planets. Mainly, that Humanity had been elevated so far beyond its puny origins that exceptional talents had easy and complete access to the fast track.
Basically, when your entire setup is an idealistic author stroking his intellectual member and going "I wish everything was super peachy-keen!", then you can't really apply the concept of the Mary Sue to things that follow that baseline.
The Mary Sue is a clumsy, disruptive and destructive force. When your narrative and cast is made up of nothing but Sues and Stus, then you have to redefine what a Sue or Stu is - for that cultural production in particular.
To put things in even simpler terms, I think Crusher is another form of self-insert or author proxy altogether, one that's INSPIRED by the first series' self-insertion fanfics and possibly is also the product of a writer who may or may not have been caught up in that aspect.
After a while, once you realize you're getting paid to handle that obnoxious kid and put him in situations he has no business being in, you probably start considering him as a proxy.
Of course, the flat, stupid and boring answer is that Crusher's probably Paramount's attempt at creating a character that would fit well for the younger viewers watching the show on weekends. An attempt at capturing a then-younger demographic with a character that sits in their age range.