Bitcoin will never replace fiat cash. A coin everyone mints at the same rate will. It will also replace bitcoin and all of the shitcoins.
Mark my words.
Bitcoin runs off the fumes of fiat.
Bitcoin is just an alternative for fiat currency everytime you need it. Also, I think there's no need to replace fiat with bitcoin because they are both significant and valuable. Both are useful, so for me much better if this two different currency will exist to help us and our economy financially.