I never hated Wesley, but I do think he was misused. The problem with prodigy characters, IMHO, is that it makes it very hard for most of the audience to relate. The character needed growth room, which he didn't get until later, after he left the show. The First Duty was outstanding for showing that. Accepting him as a very bright and gifted kid, I think it was still pushing credibility to have him working in the same job that fully trained starfleet officers generally do, flying the ship. I think he would have been much better served as part of the team in engineering, contributing, but still more closely under supervision of group of "teachers." Show him learning and a gradual shift to independence as an officer.
The only way people can accept a prodigy is if he's everyone's punching ball.