A little late to the discussion . . . on the question of whether USNA gives bonus points to legacies, the short answer is . . . they used to, sort of, kind of, but not sure they do anymore.
Two+ decades ago, kids with a close military relative were given a small amount of extra points on the theory that they were more familiar with military requirements and thus more likely to stick it out at USNA. Any military service would do and USNA legacies got no more points than a kid whose father or sister was, say, enlisted Air Force. And the "bump" was no more than someone would get for being a team captain, an Eagle Scout, scoring really well on the CFA, etc. It was something like 500 points when Whole Person Multiple scores were 70,000+. So not a difference maker. But that was then.
The above has changed for two reasons. First, there now seems to be a preference for those who are the first in their family to attend college (which would not be true of a USNA legacy). Second, attrition is now closer to 10% than the 25-35% it was in my day. Thus, the "sticking it out" argument is now largely moot.
IMHO, the main reason colleges and universities give preference to legacies is that they depend on alums for funding. Thus, if you gift $10M or maybe even $100M, one "reward" could well be a spot for your kid in the freshman class. Other legacies MIGHT give or, if legacies are turned down in large numbers, this could impact giving. [Of note, one thing a lot of civilian schools do is "waitlist" legacies with zero intent of admitting them. This apparently makes the parent(s) feel better in that their kid didn't get outright turned down but also doesn't require the school to admit them.] SAs are federally funded and thus don't "need" donor money. Of course, all SAs benefit from private donations, but it's not as if a parent is going to build the next academic building or that a SA is counting on a donor to do that.