Well, Doula hasn't done that pretty much because of the same reason Law didn't switch Doula and Trébol personalities, Doula can't control Trébol's DF and neither Trébol controls Doula's DF, just like Tashigi couldn't control Smoker's DF, Law and Luffy would have won by now, why Law just didn't do it then??
I guess from a literary standpoint that would be anti climactic but doesn't make sense considering law could do it with relative ease. Then again maybe dofla knows that move and how to counter it.
@Juiceduphody exactly.. why would doflamingo just tell luffy he has an hour to save the day why not just speed it up and find a more entertaining way to stop birdcage.. then again that would add another reason to make this arc longer..