I just don't see the poor fit as you do.
That's fair. I'm just going by examples from the show of Kim's incredibly bad record of disobeying orders. I can't find the quote/episode on the fly, but there is an incident early on where Janeway pretty much flat out tells him it's going on his record, and it's going to have serious consequences for his career. And then... he continues to have behavioral issues throughout the entire trip.
As for Wesley's Academy test, it is odd that the Academy would have SUCH stringent rules. I think that just needs to be a "read between the lines" type thing. I don't think it's JUST that Wesley was taking a test to get into the Academy. He was taking a test to get into a specifical school within the Academy. He was going for a top-level command track program.
It would be similar to applying to go to a Community College or Harvard Law School. Just about anyone can get into Community College. Only some are going to get into Harvard Law.
I don't think "Starfleet Academy" is just one single, monolithic thing. "Starfleet Academy" makes more sense as more of an organization of schools with varying levels of prestige. A doctor going to Starfleet Academy isn't going to have the same program as a security officer.
We also know Starfleet tends to be officer heavy. It doesn't work quite like a real world military does. They have enlisted ranks, but there are also ALOT of officers... it can't be THAT hard to get into the Academy. Getting to a specific program within the Academy, that could be much more difficult.
EDIT -
As an addendum to this, the idea of the different schools/tracks/levels of Starfleet Academy aren't treated like things might be treated today. Once you graduate, you just... graduated from Starfleet Academy and then move into the applicable role. Star Trek has built a culture where it would be uncouth at best to rub in how you were in x program at the Academy, like someone might stress how they went to Harvard today.
Yes, people know, and yes it will get you into better positions but... bragging about status and what not has become very not cool by that time. You don't need to specific what school or program you attended at the Academy. You went to Starfleet Academy. Your role will generally speak for itself.
Someone like Picard was likely in a similar program to what Wesley was trying to get into. He became a Captain pretty quickly. He graduated the Academy in 2327, was Captain by 2333. There some circumstances in there, but he still got it.
