I don't think Audrey was that bad at detective work. She and Donna seemed to end up doing more actual investigating than Cooper & Truman, who spent a lot of time sitting around eating donuts and getting Hawk to do the legwork

They should have just had Cooper go all Jimmy Stewart in Vertigo and start dressing Annie like Caroline

On a slightly more serious note I do wonder what TP would have been like if Lynch & Frost were able to do everything their way without interference from the network or the actors.