I think it's a misunderstanding  that fiat will be obsolete because of its elastic supply. No, there is nothing wrong in the elastic money supply. The wrong is humans just can not manage their greed through fiat.

It is also a misunderstanding that the possible success of Bitcoin is because of its fixed supply. A fixed  money supply creates high interest rate, lowering the velocity, which kills itself, said as " the one kills greed kills himself".

No, it's not true that the fixed supply makes Bitcoin possibly succeed. It is the way it produces itself, which is a better management on greed and fraud over fiat.

 In a certain timeframe, Bitcoin supply is not fixed. In the technology itself, it's not either. I think complaints about fiat for its incapabability of managing greed misleads the reason to its elastic money supply, and further misleads us from the true reasons of bitcoin's possible success.