I'm very fond of the idea of the idea of one of the themes of the story being the balance between Subtlety and Influence. You're constantly being forced to make the choice between getting things done through direct means (brutality, commands) and subtle means. The former gets things done quickly, but not always correctly (as people will subvert), while the later is a pain but can result in relationships. As you gain success, you become more Influential, but figuring mysteries out becomes harder because you're better known. One of the reason your Inquisitor has created a cadre of Acolytes is that you're not as well known (yet), so you can investigate things (and you're also expendable) in ways he/she couldn't.

Indeed. To an extent it's always been part of the game, but it's nice for it to have some mechanical effects.

Players knowing that not rolling into town with body armour and lascannons will actually make inquiry/deception type checks easier (even if they don't know by how much) encourages intelligent use of assets, and knowing that pulling out the rosettes may paint a target on you but also has a concrete benefit is likely to make for suitably dramatic closing stages to some missions.

Having run several DH campaigns, nothing tends to be as satisfying for the players as the first time they get to walk into a courthouse/barracks/bridge, slam a rosette on the table and use the words "By the Authority of The Immortal God-Emperor Of Mankind..."