Well, the way I see it is... Say we didn't have influence fall off. Now, say you're an early contributor and you quickly rack up 100 points or something. You would then get to use the weight of 100 points in every vote for the remainder of the project. However, if someone else also earned 100 points, but they did it late in the project, they'd only get to use their 100 points for the last few votes. So even though they did equal work, they received much less of a reward.

However, if influence falls off over time, then 100 points will get you about the same amount of reward regardless of when, in the project's history, you earn them (unless you earn them at the very, very end or something).