While the OP has explained they weren't 'last minute', but in December, I will echo what others have said,
@justdoit19 nailed it with the 'early bird gets the worm' analogy.
Last admission cycle our DS was done with 3 SA applications in their entirety by the 3rd week in September. Medical, CFA, FFO, BGO, and ALO interviews. All of it.
I know the academies view quality early applications in a positive light. Each of his interviewers told him so. His FFO remarked (paraphrasing here, I, of course, was not in the building during these interviews) "WOW, you are already done with your West Point app and it is September, and it's not your first choice".
It shows initiative, it shows drive, it shows that you are prioritizing things in such a way that demonstrates this process, of becoming an officer and a leader of men and women is of the utmost importance to you.
This isn't just important in terms of an appointment but can be huge in terms of nomination interviews. To be able to walk into interviews with MOC, Senator 1 and 2, and say that your applications are not in process, but complete---100% complete also can carry weight and leave an impression with the panels. I know this to be true because it was mentioned to our DS in 2 interviews.
That also goes to NROTC or AROTC applications. Having a first-round award in hand in nomination interviews also carries some weight.
This is not to say an applicant should rush through a poor quality application. Never ever do that. But I can only say that for our DS, having 3 appointments offered to him before 14 February was humbling, overwhelming, and such a relief. I don't say this to brag, at all. Nor to say he was a rock star to finish apps early. He did that on his own, I just drove and took notes. I can only say what we experienced going through this tough process and how it may have helped aid him in achieving his goal.
There are impressions you inadvertently leave on interview panels, admission counselors, FFO, and BGO's. Submitting a CFA in January, finishing an app during the winter, are things that might not be viewed in a positive light in my opinion.