More emphasis on pickup collection would allow for level designs in which you need to maintain a certain (high) speed to make the jumps required to reach the pickups, which would allow for certain kinds of obstacles, et cetera. That's a pretty common design pattern, of course.

I was actually thinking about this while playing Rayman Origins the other day; you can make it through most levels rather easily without running (or not running), but to get all lums you need to maintain momentum, time your jumps, and things like that, which certainly adds some depth. Additionally, if you manage to maintain speed and simultaneously avoid getting hurt you are rewarded with an incredibly smooth journey through the level, where you avoid traps and spikes just barely, because everything's designed around that. Speed and precision is rewarded with a tight experience, and a bonanza of pickups that are placed just so that a smooth path through the level will get you most of them, which is a great incentive.

Jazz levels more often than not are mainly about reaching the exit rather than collecting things or avoiding all traps (thanks to the five hearts you have and the abundance of carrots), I feel, which does not necessarily make the most of the game's strengths. There's puzzles, of course, which especially in user levels are pretty common, but those are pretty much the antithesis of speed-based gameplay (usually). Maybe a focus on collecting things would be a way to utilize the game's strengths.