OldRetSWO definitely brings up some excellent points. Let me add another that I've seen first hand many times.
NOMINATIONS!
No matter what your status, gpa, class rank, test score, CFA, etc. everyone must have a nomination in order to receive an appointment. There's no way around that. Getting your application completed early demonstrates sincerity, determination, and confidence. When it comes to nominations, almost all are competing for congressional nominations. Some are also competing for military related such as presidential, vp, rotc, etc. Most congressional staff begin their interviews around the 1st of November. Usually finished before christmas. If you walk in for your nomination interview, and your application is 100% complete, that can make for a very good first impression for you. Most members on the nomination board will be somewhat impressed; and/or at least take you much more seriously. Most people don't have their applications done until around November/December. Some into January.
For those who qualify for a presidential or other military related nomination, those don't have to wait. For instance, as soon as my son started the application, he had his presidential nomination. Now; just like any nomination, that doesn't guarantee an appointment. Every appointee has an nomination; but not everyone with a nomination receives an appointment.
My son went to summer seminar I believe the 1st of June. (2007 was a long time ago). When he came home, the application process was just getting ready to start. I believe it was June 15th that the portal opened to start the application process. My son completed his entire application; including the DoDMERB, CFA, transcripts, test scores, etc.... He was 100% complete. He also had a Presidential Nomination from my service time. He was completely done with the application in less than 45 days. I believe it was July 23rd give or take a day.
Long story short, he received an appointment on October 29th. He didn't need to wait for a congressional nomination, because they used his Presidential. Matter of fact, after receiving the official appointment, he contacted his representative and both senators and informed them so they could save their nomination for someone else. Now, just like an LOA, an early appointment (Which obviously can only be done with a NON-Congressional Nomination, is also very rare. But obviously, the academy review board was impressed with his application and how fast he was able to complete it. And being my son already had a nomination, and his scores were considered quite high based on many years of academy historical data, they felt confident enough to offer him an early appointment.
Now, having been an ALO, I know how the rules, policies, and procedures change year after year. But the point I'm trying to make is; in the end, you're NOT dealing with a computer. You're dealing with HUMAN BEINGS. If the time comes for your ALO interview, or a MOC interview, or the academy review board, etc. you are dealing with HUMANS. When you can walk in the ALO or MOC interview and have EVERYTHING COMPLETED 100%; that's impressive. When the academy starts preparing for application reviews, and they are coordinating with the admissions office to build a schedule, and they discover there's ALREADY a 100% COMPLETE APPLICATION ready for review, that's impressive.
So, the advantage to completing you application early, in addition to the tangible benefits OldRetSWO mentioned; is that you have the potential to impress HUMANS. I hire a lot of people in my current job. When I open and advertise a new position I'm hiring for, I usually open it for a minimum of 30 days. When I see resumes and applications coming in 2-3 days after I've opened the job, I take those applicants a bit more seriously. Because obviously, they are taking the job I am offering quite seriously to be able to be prepared that quickly.