Although the top tier candidates may not be applying at many places, they are receiving many more first, second, or even third interviews. Thus, their timing is tight in a two week window near the end of school when they start receiving offers. Near-Bottom-tier candidates may receive less interviews and are incentivized to perform more desperate acts in order to receive interviews, and thus have more time for puzzle-based applications.

But as I said, it's not too big of a deal, if they would only post ahead of time how long puzzles would be active, so one could complete them before this tightly-timed period.