Why is there so few games that includes a level leaderboard? It would be nice to do little runs on individual levels on game likes Mario and such.

Probably because setting up rules isn't always easy, especially when items carries over (think of fire flower in Mario for example)

Well, in that case shouldn't we do like, a list of all level, with different conditions, like small only, no yoshi, everything allowed, etc. ?

well that'd be a good idea imo, good luck setting that up though, must be a lot of work, especially with all the levels Mario games have in general

The problem is that I don't have the rights to do so :P

Then it's simple: ask the current moderators of the game you want to have that in. Just explain a little, i'm sure they'll understand eventually :P

Many game moderators don't necessarily want to track every 30 second section of a game. It also depends on the game's level selection capacity and ability to isolate those levels from factors in other levels. Some games make more sense than others, so there's no real guideline.