The reason nobody likd Wesley Crusher is because, frankly, the character sucked. You’d hate ANY character that was so joltingly inconsistent with the show.
Generally speaking, the characters on STTNG were pretty well developed; for the most part they were consistently done. There were some horrible errors - Picard turning down the chance to wipe out the Borg being Primo Example Numero Uno - but, you could believe them.
You couldn’t believe Wesley; he was impossible to buy. Being The Great Boy Genius was bad enough - it’s a terrible cliche - but his forced insertion into the crew smacked of a lack of imagination. “We need a kid. Uh, let’s put him on the bridge.” It defies the suspension of disbelief, for one thing - it’s inconceivable that a huge military fleet would have a kid at the helm of the flagship. For one thing, can you imagine you the OTHER junior officers on board would freak out? They’d be in Riker’s face 24 hours a day: “I’ve been in Starfleet for 15 years and I’ve been slaving away on this tub for five years and I was first in my class at the Academy and I work like a dog and I was next in line to be first helmsman and that brat’s running the ship AHHHHHHHH!” No friggin’ way.
I think Wil Wheaton’s a good actor, and it’s a shame they didn’t do more with Wesley. Had they made him more of an outsider, more of a thorn in Beverley’s side, less of a genius, and worked on his relationship with his mother and with Picard, I think we’d be far more positive towards the character. Instead, he was just the crew member who happened to be a kid - he didn’t add much to the show’s dynamic. A far better choice would have been to make him outside the crew, a kid with his own problems. The character of Alexander, Worf’s kid, was far better done; he WAS a problem for his dad, and the relationship between Worf and Alexander helped flesh those characters out far more than the relationship between Wesley and Beverley (and Wesley and Picard, his adopted father figure.) It’s telling that the only time I ever really liked watching the Wesley character was when he was interacting with Picard on a personal level.
The other problem with Wesley - well, really, it was the same problem - was Beverley. You never seem to hear anyone saying it, but I thought she was a terrible, terrible character, a sort of Saint Beverley of Sick Bay thing. She was the Gaia Mother of the ship 19 episodes out of 20; most of the time she was the perfect mother and the galaxy’s most caring and perfect healer. I didn’t buy her at all, and that contributed to the weakness of Wesley’s character.
I always bought the idea of having families on the ship. I think it could be reasonably hypothesized that given the nature of the duties asked of Starfleet personnel, and knowing what I know about military service and the attributes of good soldiers, that the increase in morale and productivity would more than compensate for the added risk. I think it’s quite reasonable to surmise that values in the 24th century would be sufficiently different that they’d take this risk. And in MOST cases the family angle was really interesting: Worf and Alexander, or O’Brien and Keiko. They just blew their chance with Wesley by making him a kid genius. The whole “Ender’s Game Ultra Genius Kid” thing is too hackneyed to work on a weekly show.