You know the thing at the end of the game where it says "Stage Clear" and that says 100%. Getting that, is what All Levels is.

Doing the Time Attack stage is the end of 100%, it's obviously clear that isn't involved in All Levels otherwise...All Levels would be simply identical to 100%. The issue with calling it All Stories, is you simply wouldn't have to do all the levels, as all the paths are not required to finish all the levels. Hence, All Levels makes total sense.