Do you propose these shenanigans don't cost them a pretty penny? You do realise corruption involves bribes?
What would you guess is more expensive, Bitcoin transactions or bribes to various bankers, accountant & state officials?
What do they do when they transfer these bitcoins to their other rich friends, have them transfer them back to them? If you want to use them, you'll have to convert to a real-world currency which can be spent and then you're back in the world of bankers anyway.
So your way is Clandestine $->
BTC , $4 transaction fee then clandesting
BTC->$
Or just go with the clandestine $ shenanigans anyway.