Not all places are like that, I believe there is probably 1-4 cadets that are home-schooled as there are few opportunities to excel or prove yourself in. I think the others are probably club sports or martial arts participants
Virginia is one state that does not allow homeschoolers to participate in public school sports. My ds has had to work hard to find opportunities to compete (in fact that was the subject of an essay about an obstacle he overcame). Those have included club sports such as basketball and rugby, and a cross-country club that competes against private schools and other clubs. He also had to determine to be fit on his own (shows discipline), and he did very well on his PFT.
My ds does not have an appointment yet. He has presidential nominations because of my dh's service, and he also received a congressional nomination from our very competitive district in Northern Virginia. He also has been offered a type 1 ROTC scholarship, so obviously he is competitive. I would say you are right--there are going to be less qualified homeschool candidates simply because if their parents do not have military experience, then they often do not really know what they should be aiming for academically, and it is easy to fall into the trap of, "well, we're doing more than our local public school . . ." My ds has desired to be an officer since he was young and we were stationed at USAFA, so that goal has always guided his educational choices and provided motivation for him. We started a rigorous homeschool co-op to be able to provide AP classes and other advanced or more in-depth classes, because we weren't happy with the high school co-op offerings around us, and we couldn't afford all on-line classes (and didn't think an entire high school career of online classes was the best option anyway). I have my kids take standardized tests (AP or SAT 2) in as many subjects as possible to validate "mommy grades". We had ds take calculus at the community college this year to show he can handle college-level classes with no problems, although financially that wasn't an option for all his classes. These types of things are what homeschoolers do to show they are competitive, and I bet there are more of them out there that you think. Just from our circle of friends, I can think of probably 10 kids who are at or graduated from academies in the past few years!
Oh, leadership--my ds is heavily involved in Civil Air Patrol, but most of the other homeschool kids at academies that I know did boy scouts. I think that you probably have to have one or the other, or something like JROTC, to get an appointment as a homeschooler. Ds also found other areas in which to lead--for example, he helped found our chapter of the Homeschool National Honor Society, and he is serving of president of it this year. He is also in charge of our co-op activities club, planning field trips (making sure there are appropriate activities for all ages in our co-op families), social activities, service activities, etc. He coached a youth basketball team. Heck, he's the oldest of 10 kids, so he's had a ton of natural leadership experience already!
Again, knowing the kinds of boxes admissions people are trying to fill helped him know what kind of activities to make happen. I don't think it is any different than having to attend a poorly-performing high school, where you have to go out of your way to make sure you are challenged. For homeschoolers, you have to go out of your way to make sure you are challenged in all areas--academics, sports, and leadership--and I think it is impressive to academies to see kids who are not just going with the flow, doing the things they are expected to do, but are looking for ways to lead and challenge themselves. I hope as more homeschoolers are accepted to academies, more homeschoolers coming down the pipe will see what they need to do to be competitive. And there really are more and more homeschoolers in the general population now. It's a good option, especially if your local schools are underperforming, or if your family moves/travels a lot, or a bunch of other potential reasons.