At the current stage of development, Fiat is absolutely necessary. Perhaps for the real functioning of the economy, Fiat is not needed, but the consciousness of most people is still very attached to the Fiat. So it was with the first paper money, then with electronic payments.
What do you mean by "real functioning of the economy"? It is generally accepted that any advanced economy, where advanced is anything beyond a simple subsistence economy, money is a must-have, as it were. In a subsistence economy you don't really need money and can get along with barter as it doesn't introduce division of labor other than hunting, gathering, and agriculture. Anything else needs money, and modern economies need fiat as money because money based on hard assets will be ineffective in so complex economies.
The "built-in mechanic" of fiat regulating itself is a complete fantasy. Central banks and governments set interest rates, expand the money supply, established the rules of FRB, create bailouts, maintain liquidity, etc. There is nothing "built-in", nor "automatic".
Of course all of the features you mention can be implemented in cryptocurrency, as well.
You may need to finish school, really. And learn about the forms in which money exists today. Central banks and governments on their own can't "expand the money supply" as it will only cause inflation, price inflation. Hint, you may want to read about endogenous money supply.
Yeah fiat currency is very necessary for a government and for the people. Most businessmen are using fiat currency for their transactions. It will be there although cryptocurrency takeover the market in the future. After a long time when all the people in the world will use only cryptocurrency for their daily needs and for their transactions crypto may takeover fiat currency.