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.
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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.
The "market cap" of Bitcoin is not currently greater than $1 trillion. Therefore it will never be greater than $1 trillion. Therefore Bitcoin will always be an alternative currency. Q.E.D.
http://www.automizeit.com/blog/wp-content/uploads/2012/10/guinness-brilliant.jpegBitcoin's market cap could absolutely exceed $1trillion. It isn't a near term goal but 10-20 years from now, who is to say it isn't possible? The market cap is a direct reflection of the value it's holder's give it. If the market cap isn't large enough for individual holder's to maintain a sizeable portion in their wallets (i.e. enough to make daily purchases, receive wages, pay taxes, pay your mortgage, have a savings, etc) then it cannot ever replace FIAT. There are other obstacles mentioned in this thread as well.
If 15 years from now, bitcoin is worth $40,000 USD per coin, the market cap will be roughly 750 billion. That means 1 billion people could hold $750 each, or 10m people could hold $75,000 each to put it in perspective.
