The idea is to have a very simple score system that encourages level replayability without affecting gameplay within a level in any way.
In particular, when you pass a level, the number of points for that level is equal to the number of levels passed (including the level just passed).
When you pass a level that was already passed, your level score replaces the previous level score.
Your total score is equal to the total of the level scores.
This encourages replayability of levels since you can get more points for passing a level as you pass more levels.
Do you think this idea would encourage players to replay levels and compete on a leaderboard for (total) scores?
Now, if you also could make them slightly harder over time (might not be too hard in a game with enemies. You could make them a bit faster or smarter), that might work.