It is just one model to look and compare players. Like most models, it gives an incomplete view of players.
It is a tool, not the end all be all of player rankings.
Yes, it's a model, but it's particularly bad at doing what it's supposed to do: measure the efficiency of a player.
And, let's face it, most people use PER as an end all be all measure of how good a player is. As somebody else pointed out, the fact that that it's based on how many shots a player takes makes it pure garbage in achieving that purpose.
It's insane to me how little efficiency is valued among pundits and fans, especially considering it's one of 2 factors that determines the outcome of the game.
(# of possessions) x (points per possession) = final score
He with the highest final score wins. Therefore, the only way you can make your score better is by shooting more efficiently, making your opponent shoot worse (defense), getting more possessions (rebounding), and reducing turnovers.
Efficient shooters help your team win. Low percentage chuckers don't. PER rewards players for chucking, and therefore, it's pretty easy to say that it sucks as a model.