From a designers perspective.
it's a get_recognized/win situation for a designer to inject last minute cooked up designs since it escalates them up through this list:
https://logotournament.com/logodesigners (points tab)
In fact if it is out of a fear of a design being stolen then that's a 3win situation and I don't think last minute uploads would end their days naturally, nor anyone would see a benefit not to Last Minute Upload.
As for the CH side of things.
There might be a case when CH actually locks on a concept/particular design long before the submission deadline and doesn't bother making decision about other submissions or ending the contest as soon as he knows what he wants. Does it come from the notion that "maybe..." there will be something worth the sum I'm willing to pay? I don't really know. The way I see it the only thing that comes after "maybe" is another "maybe" which only makes CH fall into his/her own uncertainties. If that's the case CH shouldn't be irritated or be blaming Last Minute Uploaders and end the contest appropriately.
My view
Contest time span can be used from it's start to it's very deadline, that's what the span is for. I will upload if I feel I have something worth showing even at the very last minute.