Did I stay up with the classes? Well, not always — some of them I caught up during breaks. (That's the advantage of end-of-year not end-of-semester exams, too.) But did I know the material by exam time? Yes.

But look, more generally, you say you have to "incentivize" students to keep up but I think we agree that it's in their long-term interest to keep up with or without graded homework, so we're talking about behaviourist incentives not rationalist incentives here. And with that admitted you have to consider that there's broad scope for other ways to incentivize than through GPA consequences. (I mean, hand out candy, or pizza, or Pokémon, or porn, or whatever this year's students are into, you can probably think of a much better ideas than these.)

^Unless you were that one kid who had mono during finals week. But that's a different issue.