How is the Fed supposed to manage the bitcoin supply? Buy up 30-50% of the coins that exist? Where will they get the money?? Supply and demand would set in big time and the amount of US dollars required to buy one bitcoin would skyrocket.
They can adjust the supply by changing the reserve requirement.
And that buying a large number of bitcoins to hold in reserve would be expensive is irrelevant when you can print as much money as you want. They already print more than 10 times the Bitcoin market cap every month.