You play as Officer Cole Phelps of the Los Angeles Police Department and as you play the game you move through the different police rankings and move to different assignments in LAPD.
Sure you act as a detective in a detective game in L.A. Noire, because you are a detective, but at the same time a cop. So therefore it's both a cop and detective game.
And of course my point still stands, the very idea of GTA games doesn't mesh with playing as anything other type of cop than a corrupt cop and that defeats the purpose of your idea altogether.