But I think the trend is now changing, as people are adopting bitcoin not only for investment purpose but now many people are using bitcoin as currency, they use bitcoin not only for online business and shopping but now there are so many places where bitcoin can be used for shopping like in local shops also.
No matter how many people adopts bitcoin or use it as a currency but it would still not be able to replace fiat, people all over the world have been using fiat for centuries, so even if they find something like bitcoin to be used they will still give importance to fiat so the price of bitcoin thus reaches too high but it wont make fiat worthless.
Sure fiat is at the control, the bitcoin transactions arent near to achieve 1% the fiat transactions, and this is something that wont change. The value of bitcoin wont make any effect over fiat besides the exchange from bitcoin to fiat.