ever increasing number of home schooled students. To the contrary, if they were incapable of demonstrating good leadership skills, the SAs would be decreasing the number of appointments going to home-schooled students.

I would characterize your experience as anecdotal and not representative of how the SAs feel about home schooled students. The figure tossed around by the SAs is that that the investment over a 4-year period in each cadet/midshipman is around $400,000. They would not be putting that kind of money into home school students who were busts as leaders when leadership training is the purpose of the academy experience.