Fiat will not be worthless as long as you can exchange it for good and services. In order for fiat to fall we would need a gigantic event that would be studied thousands of years from now at a roman empire fall tier of happening. We are talking about the biggest fall of empires ever.
Yes increasing the value of bitcoin cannot make any changes what so ever on how fiat being used,becuase its not about the price,its about how many peoples accept in all over the world,and increase value of bitcoin to $10.000 or even more would not make it take place of the fiat currencies.
Yeah even if price goes in millions then also fiat will always exist as everyone prefers to use fiat as it can be used everywhere easily and even it holds support from the Government.