You can't eat a dollar too. Intrinsic value of a dollar is smaller than a piece of paper, as it's not even that good for taking notes. It's valuation is the same: based on artificial demand.
The point of the dollar is, that it is backed by the United States of America. By the government the Federal Reserver Bank as the front line of setting and defending the value of the dollar. And by the whole US industry, which is trading their goods in dollars. That is the reason why modern currencies are generally valued vs. the gross domestic product of countries.
Yeah, I'm pretty sure that Federal Reserve hasn't been really backing the dollar. The gold is there, sure, but it isn't connected in any way with the value of dollar. The Federal Reserve surely doesn't have enough goods to back all of the dollars in circulation. The fact that US industry is trading by dollars doesn't change the matter. There are quite a few businesses that trade by bitcoin.
The dollar has not been backed by gold for a long time. It is backed by the Federal Reserve bank by the political power of the US and of course by the GDP of the US. Like with gold prices, there is quite some flexibility in the value of a currency, but that flexibility is contained in certain intervals because of the influence and the acting of the Federal Reserve bank. As long as the US doesn't default, the dollar has a value.
I get your point and generally agree fiat is not backed by much more tangible than BTC’s math. To be fair, plenty of people trade US dollars for US political power. Lobbying, 500k speaking fees, PACs, Charity “Foundations”. You and I can’t trade in those markets because we don’t have enough dollars (or have too many scruples)
It is backed by the GDP as you can buy goods sold by US producers with dollars. Be it iPhones, beef, corn, cars, airplanes.
And you would quickly notice the US power when you tried to print your own dollars for example.