Pritzker is the only school that has been so explicit in describing how much being late hurts an applicant in numerical terms, but all rolling admissions schools say pretty much the same thing on this topic - the earlier, the better. Why do people want to bury their heads in the sand over this? The later you submit secondaries (the later relative to when an individual school first released secondaries), the steeper the hill...
I agree with something you wrote - you really do only have about one month or so to be "early" and in the first big wave of applications and completed secondaries. I read the stats somewhere, but you might be surprised at how many people are complete relatively "early." Can't put my hands on it, but it is something like 25 percent of all applicants...
Whatever...believe what you want to believe about all of this, but being "average" when it comes to med school app completion is risky...being "late" is deadly...as far as I am concerned, if you aren't early, you are late...