It is not the US Fed (federal reserve) which exchanges crypto to USD but the commercial bank which has the fiat holdings of stable coin issuers.
For ex. for USDC / Circle it is Silvergate bank.
The total amount of fiat held by bank of stable coin issuers is less than $100 billion , but the total crypto market cap is $2+ trillion.
In case of mass movement to cash out from crypto to fiat it will be the commercial banks who will decide to deny exchange of crypto to fiat - it order to preserve some of their holdings.