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.