I want to point out that the OP's question was whether Bitcoin could or should replace FIAT.

The answer is a resounding no.  Bitcoin is a substitute or alternative currency.  It is a global currency and an online currency, very much unlike any of the current forms of FIAT.  This is where it's primary strengths lie.  As the economies of the globe become significantly intertwined it makes sense to share a simple and easy way to make transactions and spend between countries. No other currency allows for this in a simplistic manner.
 
FIAT of other countries will remain the base for determining the exchange rates between countries....  Bitcoin is no where near large enough to operate as a currency of scale on a stand alone basis.  It's value is going to be derived from the other currencies of the world as it changes hands.

Bitcoin is significantly less expensive for businesses. There is no risk of chargeback and the fees are exceptionally lower than standard payment methods.  You can't ship cash to pay for something online. There is also a very low risk of fraud.  Without more research, it is hard to say if it is a safer form of payment for businesses than accepting credit cards but I would venture to say there is far less fraudulent activity in bitcoin purchases than credit card purchases.

The benefits for business, the ability to be used globally, as well asthe low risk of theft and ease of use on the internet are all factors to promote the adoption of bitcoin AS an onlien currency.  Not necessarily a replacement for FIAT....

That being said, Bitcoin isn't even large enough to support replacing a FIAT.  If it has a $1billion market cap, then 10 million people could each hold $100.  That is not enough to support a population in standard trade.  The market cap would have to exceed $500b to $1 trillion to service a large portion of the global population.