Eh, never hated Wesley back when the show was airing. When the episodes where he's badly written (and there are many) are spread out over weeks or months, he's not annoying enough to hate, and he does get some okay writing here and there.
If anything, having a younger crew member helped teenagers and kids find a more relatable character to have an in to the show if they weren't already fans of TOS and the movies. So in that , even though he was poorly written most of the time, he's still a valuable character.
Honestly, even back then my impression was that the writers were just crap at writing a believable "gifted" kid. That Wesley was supposed to be even more than gifted didn't help because getting the kind of personalities that form around kids that really are that much smarter than those around them isn't exactly a common experience even among gifted kids. The kind of genius that Wesley was described to be is just too rare for even the mensa set to have a lot of experience talking to.
That's what I think the problem was. You had adults that weren't used to the kind of intelligence Wesley was supposed to have, and didn't really remember being Wesley's age trying to write him. They just used tropes and guesswork to turn him into what amounts to a DMPC, a free check to make bad writing choices via "super genius saves the day" vs "teenager fucks up" mismatches.