Also, that point of view seems to assume a linear story to some extent. ...or, well, a preset story. In a game where neither is the case, it is my opinion that it fits less.
It doesn't have to be a linear story to still have the problems of believing there's a direct correlation between Level and actual ability and power within the fiction. After all... there is no timetable on leveling up. It can happen as quickly or as slowly as the DM decides based upon the XP he gives out. Which means you can effectively have PCs gain levels over the course of DAYS, if that's the way the DM is running his game. And thus we're supposed to believe in the fiction (if Level is supposedly a true indication of a PC's ability and power) that they've suddenly gone from being barely able to take on a kobold on Sunday to now going toe-to-toe with an ogre on Saturday? That makes no sense either.
Trying to use Level as any actual indication of power I still think is futile. Levels are a metagame concept meant to give the illusion of characters getting better over time... but which hold barely any reasonable facimile to a realistic portrayal of that process. PCs just get "too much stuff" due to the game mechanics in place so that gaining "levels" is actually interesting for the players.