yeap it affect alot
even the mandatory function of itself is the fee
If it hit $10,000 per bitcoin, the fee will be huge
If the price goes that high then I don't think that people would be worried about the fees and will be willing to pay even higher fees as they will start selling their coins and will convert to fiat as that is the only choice people have to spend their bitcoins.
Why go to Fiat? If the cost of bitcoin is very high, then the infrastructure will start to develop much faster. We will be able to buy everything using bitcoin. Fiat will be outside this chain