There is not one fiat currency. They actually all compete against each other. All of the fiat currencies' tied to the trust for the governments and their economies.
For example value of gold is pretty much same as it was 2000 years ago. Prices of gold change, but value remains almost same. There was no USD 2000 years ago.
In this regard bitcoin is playing role of gold, it is actually better than gold. If USD collapses another currency will take over. Bitcoin will keep its value. Prices are not going up because of fear, rather decline in supply and people realizing it is better way of preserving their assets.
I think bitcoin price is stuck at 2500 right nkw because of fear what will happen with forks. USD cannot destroy bitcoin. Only bitcoin community itself can destroy it.
Final note, as long as there is electricity and internet, crypto will continue getting stronger and be around for long time.
I have not said anywhere there is only 1 Fiat currency?. If the U.S economy collapses, do you honestly think the world economy as a whole would be fine, and that Bitcoin would remain at '$2500'?
Bitcoin is not Gold, and never will be. Gold can be traded physically on the streets. If the 'world ends', people will be trading Gold, Silver and Copper as I reckon the lack of availability of Starbucks WiFi may hinder the long and expensive Bitcoin transactions.
Bitcoin's price is generated by the total mean price against all currency trades. When It has it's own unique price, in which my house will say be worth 150 BTC and not £300k , then I will agree with you more. Until then it remains inflated and controlled by the world economies.