On the first hand Bitcoin will never reach that value and we have to be realistic and not dream because this is all wasted time if we talk about that it will reach the $10,000 so stop it also.
And no Fiat will be not worthless if that is going to happen but first you must let it happen and than we all can talk futher, the price is not even rise in the halving now.
Right 10,000$ in only in his dream because we know that the price of bitcoin can not reach that price.
Fiat is can not be worthless because you can not use bitcoin directly to buy you want you need it first to convert it and use fiat to buy things.
Yeah fiat will always be in demand even if price of bitcoins goes that high as we need fiat to take care of our day to day transactions and that can be done only by exchanging bitcoins to fiat.