It seems to me that a student who did the work early, but then sat on it for some reason (maybe to polish it), is very different to one who did the work at the last minute - even if they handed it in on the same day.
Even if you have a proposal 95% complete months early, there's no real benefit to submitting it, and some value to waiting - to polish, or perhaps to amend the proposal for a changing world. I've certainly seen professors go back and rework proposals at the last minute because someone else had published related work they needed to account for.
The other issue that came to mind is that people finish work near deadlines with procrastinating, because work takes time. If there are two proposal deadlines per year, and the average person takes ~6 months to write a proposal, you'd see a normal distribution ramp-up of submissions, and never see the declining count because those people missed the deadline.