No one said he's important to them either. All I said is their reputation is at stake because a man seen as a marine hero was kidnapped by a pirate. If you genuinely believe the WG doesn't lose face from it, then there isn't much I can tell you to convince you otherwise because it's supposed to be common sense.
And I don't get why you're acting like I said WG is going to fight a war to save him. I simply said BB might use him to get something he wanted from the WG, and the WG may comply to save face even if they don't care about Coby. A cover-up is harder than a simple bargain, then they can report it however they want since BB won't care.
You don't deliberately let mistakes happen just because you can cover them up. That's too stupid. The WG already lost its reputation and lost kingdoms and people's trust. That's why the likes of Morgan are defying them so openly. They can't afford to make more mistakes. Coby's kidnap is big news whether they care about him or not. And they must to something about him if they don't wanna come across as weak.
The WG cares far more about its own reputation that it does about the marines', the Gorousei made it clear to Sengoku and Sakazuki when dealing with the Impel Down and Doflamingo issues.
And as far as we know they have far greater concerns that dealing with a reputated but otherwise still secondary marine captain, that isn't irreplacable to them.
The only way they could ever agree to make a deal about Coby is if they feel he's really an extremely important asset, or do think he has vital informations about them that they can't reveal.
And Sakazuki is extremely hardly someone who'll make deals with pirates, we already saw that with the Bonney-Blackbeard situation after Marineford, with Bonney being strongly implied to be far more important to the WG that Coby currently is.