No I don't think it will replace fiat as the governments just won't approve due to the lack of control they can have with Bitcoin. But hey I can be wrong, anything can happen in this strange little world.
The development of bitcoin has increased, and more and more are familiar. The bitcoin transaction is very easy and fast, I think it will be a tool for transactions like banknotes, but little possibility to replace fiat money. because the government has the right and authority in each country.
No chance bitcoin will replace fiat money in terms of future banking, its because government will not allow it to happen. And also banks will not accept bitcoin because banks wants constant earn of profit. We know that bitcoin is volatile, it means that its price is rapidly changing and its unpredictable to know if its going to increase or decrease, so banks and governments will not bitcoin to be the future of banking.