Hi doma,
Fiat does not mean faith. That is the word fides. Fiat is from the word facere, meaning to do. Fiat means "let it be done".
A fiat currency is backed by authority rather than by a particular asset, or indeed faith. The government confers legal tender status on its preferred medium(s) of monetary exchange and/or storage. The value of the currency is derived from the fact that a sovereign authority makes law and has taxing powers over a population of productive, property-owning, income-earning citizens. The exchange value of money is derived by comparison of sovereigns. The property people own is of all sorts of types, not merely gold. Value accrues to different goods and services in proportion to their utility, their scarcity and the demand for them. Currency is the medium by which people exchange goods and services amongst themselves. The market and/or the government sets the value of goods and services against the value of the currency.
It's a big machine expressing the value of all sorts of things that are bought and sold within an economy.
To create a situation in which money has no value, you have to have a central bank with little or no credibility. This is not the case with the US. It does not require a war to give the US dollar credibility as a valuable medium of exchange. It requires a relatively productive economy.
Is it a perfect system? Of course not. Democracies make economic mistakes, just as tyrannies do, though they are apt to make modifications more readily.
Is it better than a gold-based system? Of course. Gold makes a reasonable store of value but a lousy currency. But there isn't enough gold to support the value of all transactions. All the gold in Fort Knox would be a tiny molehill set against the mountain of the US economy. So you need a much larger base of valuable assets to support a currency. Fiat money reflects this much larger asset foundation.
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