I mean if he saves the day how is it unearned?

In the first couple seasons, the rest of the crew would suddenly become wildly incompetent to justify Wes being the one to save the ship. The show got much better about actually giving him strengths to play to later on.

I didn’t especially hate Wesley, but I also didn’t enjoy his character. Part of it is that the narrative often framed Wesley from the perspective of Picard, who often seemed to be irked by Wesley, priming the audience to feel the same way. In many of his earlier appearances, before he was a cadet, I recall some Wesley plots involving him being over-keen and meddling with things he shouldn’t. But it all turns out fine in the end, because Wesley is so precocious and special. This is likely a reductionist and possibly incorrect summary, but it’s how I remember it.

When I try to think about faults or arcs that Wesley had in TNG, I really struggle to think of anything that made him feel like an actual character. There was an episode where he was considering giving up after doing badly on the academy entrance test, until he had a rare bonding moment with Picard. Then there was the academy shuttle crash coverup in which Wesley doesn’t feel like he has any real agency or real conflict for his character.

I agree with you that his key role was about giving the family aspect, which I think was useful, but especially when combined with the young genius trope, he felt more like a prop than a real character (part of this criticism is also aimed at how they explored themes of family through Beverly — I see what they were going for, but it didn’t fully land for me).

Now that I’m writing this, I’m thinking of episodes I wish I could’ve seen to develop Wesley more. Such as a “Lower Decks” (the TNG episode) style look at other young people on the enterprise, before Wesley is allowed on the bridge. I could see him framing himself as having more access or knowledge than he actually does and lying to make himself seem impressive to his peers. Then he gets peer pressured into doing some dumb stuff to gain that access he pretends to have, and it causes complications that threaten to reveal Wesley’s deceit to both the crew and his peers.

I’m just spitballing. My main point is just that he seemed simultaneously overused and underutilised — for the screen time he gets, he doesn’t really get to be an interesting character. He doesn’t need to be edgy — idealistic boy genius who can’t wait to join Starfleet fits in great with TNG’s general tone. However, without something to temper the optimism with, TNG could be saccharine sweet.

And yet, he would give it all up…