Fiat will exist as long as governments will do, and people will be forced to use it if they are going to pay taxes or get paid themselves for offering their services in the public sector. Therefore, I don't think it is quite correct to say that there will be totally no reason to use fiat. Governments are powerful and as long as they remain so, they won't accept Bitcoin as a viable alternative to fiat money. I mean, for example, as a legal tender for paying taxes.