Yeah, I'll agree that Wesley was a bad character not because of his age, but because he was badly written.
Had Wesley been a fresh-faced naive new Academy graduate, he would have been Harry Kim.
Had he been a former head-of-the-class Starfleet cadet, who had been dismissed over disciplinary problems or some controversy, he would have been Tom Paris.
The idea of an underage civilian on the ship who has far more skills and knowledge, and better instincts, than the average civilian kid, was not a bad one to start. Having Wes show potential to one day become a great Starfleet officer, and having the crew train him and mentor him, especially Picard, was a good idea.
But in execution, Wes was a disaster. Part of that was that, beyond the sub-standard writing in S1, the show also suffered from a terrible lack of any directing talent. Any director who couldn't get a decent performance out of Patrick Stewart or Wil Wheaton didn't deserve the job, yet the entire cast turned in awful performances in S1, and that's a result of bad direction.
As we saw later in the show with some of the less talented cast members, a good director can get a good performance out of even a mediocre actor.
Comparing Wes to Jake Sisko is apt, as well. Both were played by exceptionally talented actors, both characters had lost one parent in a Starfleet-related action, at around the same age (Jake was a few years older when his mom died), both had commanding father figures played by equally talented actors off of which they could play a lot of scenes, and both were around the same age at the beginning of their respective shows.
The big difference, of course, was that Jake was written as an ordinary kid, not a wunderkind or boy genius. And as such, Jake had the benefit of writers knowing him better when they wrote him, because as far as I know, none of the TNG or DS9 writers were Pulitzer winners in high school and so had absolutely no experience to give them Wes' perspective.
Jake's journey from unsure kid to burgeoning writer to successful journalist (and, it is expected later, novelist) was far more realistic than Wes' entire concept, and showed far more of what the average Human was supposed to be like in the 24th century. He was a more successful character and gave a far better insight into the Human race of the 24th century than the uberkind Wes, or even any of the Starfleet characters in any of the shows.
Too bad Bev couldn't have adopted Jake Sisko.