The Naval Academy has never advertised nor explained the mechanisms that "trigger" the offer of an LOA. It's not something they discuss. There's no "triggering" mechanism. Simply completely all requirements and doing well in all areas does not "trigger" anything other than put the candidate in the "triple qualified" category (academically, physically & medically) - a minimum requirement to be considered for an appointment. There's a crowd of outstanding candidates, many of whom will never get offered an appointment even though, on paper, they are objectively "more qualified" than others who get offered an appointment. There are a host of reasons as to why this happens. Oftentimes it's simply a matter of geography. Somebody has to get an appointment from Idaho's 2nd congressional district. They may have attended a small, rural high school with no AP programs and limited opportunities to play sports and extracurricular activities; whereas not all the candidates who applied from Virginia's 2nd congressional district (extremely competitive!) will get appointments even though many of them have a stellar candidate packet. There are sports considerations. There are special considerations for outstanding candidates from "under-represented areas", which is admission's code for "diversity." Some candidates have an unusual background, a story, that makes them particularly appealing to the Naval Academy for some reason other than grades and how far they could throw a basketball in the CFA.
Would there be a reason for the LOA, you ask? Sure! Does that mean one will necessarily be offered? No.
It may seem like LOAs are being handed out like candy by reading this forum. Candidates are proud when they get them so they often share the good news with others. Nobody is proud of their TWE. People tend to discuss good news more than mundane or bad news. It's why we sometimes feel inadequate when we peruse a friend's Facebook page. It's a "highlight reel" of their life! You wonder, "Why aren't I snow skiing in Vail?" - "Why aren't I being invited to all these parties?" - "Why aren't I white water rafting in Colorado?" - "Why don't I go on wine tasting tours?" - "I have never been to Rome and seen the Coliseum." Nobody posts a picture of themselves, wearing grungy clothes, sweating and say, "I spent all day doing yardwork and it was a miserable 100-degrees outside. I got a nasty splinter in my hand that hurts like hell and I have some weird blemish on my left shoulder that has been there for a month that I think my dermatologist should look at."
LOAs are still rare although it may not seem so by reading this forum. The vast majority of candidates who get appointments will not get an LOA.
By the way, once these successful candidates get to the academy nobody is going to care (or even know) that they got an LOA -or- that they got a presidential nomination -or- that they maxed out in pull-ups on the CFA. Nobody even talks about it - and, like I said, that's because nobody cares.