We will have to see about the "arbitrary". If if want to convert 1Mio$ to BTC send it over and my friend on the other side wants to convert it back to $, what would happen to the Market?
That's an implementation detail, not a limitation in the Bitcoin protocol. But in any case the implementation is catching up to the capabilities of the technology every day.
I'm still waiting for a sheikh (or two, the more the merry) to suck up a million coins and then guarantee to sell them at price X+5% and buy at X-5% for the next year, as long as supplies last. Would give us a great transitional phase with lots of people (arabic or not) getting into btc i guess. In a sense, that would be the ideal situation to increase adoption.
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?