I think that the brightest ideas are most probably the simplest ones, and yet it's so hard to come up with them. I agree with the big pot idea. I will try to address some of kojackers concerns.

Presenting the entries can still be done in categories. After all even the repositories need a category for submission so this imo is a non-issue.

The incentive for developing something apart from System/Utilities is that it is going to get more votes exactly because most utilities are already covered.

The other concern (about incentive to try something new) is legit, but it does not seem to be affected by the existence of categories, as not every developers comfort zone is the same. However we could come up with an incentive for the new. For example award 10 more points to apps from the missing list, or apps with no competitor (no other app with similar functionality).