I think there are rules governing what the Denarians are permitted (by Heaven) to do. You are only allowed so many tricks and Anduriel had to give up his body morphing slot in order to get the Animate Shadow power.
Consider the one thing none of them are allowed: they cannot edit the host's perception so that he never hears a Knight's demand for him to give up his coin. He might accept (Cassius) or reject (Rassmussen) it, but the Fallen can't take the choice away from him.
I wonder what Lasciel's alternate form would have been if she had gotten control of Harry? "Hey, I've been turned into a woman. Damn I'm hot!"
I think the coins give them more leeway. Remember that some of the Denarians have names while others are referred to as their Fallen. It was explained by Nic that some of them retain a measure of control, while others are completely taken over. Though I think the holder has to in an extent relinquish control to the Fallen in the first place.