As shown; every cadet and family is different. Each has different needs and capabilities. So while I think it's good to ask advice online in the forums; the "RIGHT ANSWER"; at least as far as I'm concerned; if for you to sit down and speak with your parents about it.
My family is military. My son (C2C) was born overseas on a military base. He moved around to a few military bases. Same with my daughter (Who is older). My son's entire application process was done "As a family". He did all the actual leg-work; e.g. lining up teachers, getting the CFA done, taking the SAT/ACT and getting all his grades/tests/transcripts/etc... submitted; etc....; but he kept the entire family involved. Bounced ideas off of me for my 21 years of military experience, plus my knowledge of the application process. Talked to his mom about other post-high school options and advice. Talked to his sister (Who was starting her senior year are State University) to get her perspective on college. He also had to bounce the whole Sports thing to. He received his appointment in November, but shortly after was also recruited for football. He was also offered football opportunities at other colleges.
Point is; a military family tends to be "Closer" than many non-military families. When you move a lot, you leave behind your closest friends. Both children and parents. Parents and children of military families many times become each others best friends. My wife has always been my "Best Friend". Until college and my son went to the academy, he and his sister were each others "Best Friend". They still spend hours a week talking, Facebooking, etc... with each other. So for us, it was natural that we would all go to the academy with him on "I-Day". Then again; because we're use to it, we knew there'd be no crying from mom/me until we left. (Yea, I cried later on, by myself). Another advantage we had is that we're only 2 hours from the academy. So we also showed up for "A-Day", "Every Parent's Weekend", "Season Ticket holders for every football game", "him coming home to go deer hunting", etc... Basically; we see our son about 10 times between August and Christmas. Spring is a lot less. But even if we lived across country, our family would have been there for "I-Day, A-day, and Parent's Weekend".
But that's the point. Each cadet needs to talk it over with their parents. It's not ALL ABOUT YOU. You might think it is, but that's just your perspective. If your parents WANT to take you to the academy, and they have the means to financially, then you really should consider allowing them to. They need transition/closure just as much as you do. Talk it over with them.
I admit that the 2 hour drive from our house to the academy on "I-Day" was the quietest day in our family's lives. Little if anything was said. There's nothing to say. Does that mean that it was a waste for us to take him there instead of him going on his own? No. He knew we were supporting him. He knew we were there for him. Even if nothing was ever said. He also knew that WE NEEDED to do this. But again; we're a military family. It's different. Can't really explain it. But it's different. Anyway; hopefully anyone who needs to make such a choice come "I-Day" will talk it over with their families. It needs to be a "Family Decision". Best of luck.... mike.....