Unfortunately as the overall supply of new coins diminishes, nobody would want to do that, as other parties would probably buy and hold. In conclusion, we might always have to pay a large premium when shuffling large amounts of fiat through btc., be it because of fluctuation or uncertainty in price or due to costs related to the circumvention of money laundering regulations. The question is: will that be cheapter than what we do today? How much is not having to trust anybody in the middle worth?