As of July 2013, currency in circulationthat is, U.S. coins and paper currency in the hands of the publictotaled about $1.2 trillion dollars. The amount of cash in circulation has risen rapidly in recent decades and much of the increase has been caused by demand from abroad.
So we still have a long way to go to supersede fiat currency. The thing is, fiat cash is being printed like toilet paper and it decrease in value, where Bitcoin increase in value. ^smile^
For me Bitcoin doesn't need specifically to take over the system of cash or fiat. Because as you said dollar or what we consider paper money has a lot of circulating portion around the world and it is consider as a universal current in terms of fiat. So I think Bitcoin much need to develop its system to make it as a more universal current compare to fiat. Serving a better option on transaction specially on investing and trading.