No, they are not just sitting idle, the Fed needs that money (and it needs to be liquid money) to do it's job on a daily basis, in the same way a company needs a checking account.
Gold is certainly sitting idle.
The don't invest in stocks or other volatile illiquid assets for this reason.
What's "illiquid"? Lol. You mean non-saleable? Bitcoin is the easiest asset to sell at the market price.
What is wrong with just letting the free market decide the price of Bitcoin? Why do you need the government to compel taxes from citizens in order to prop up the price?
There's absolutely nothing wrong with letting the free market determine the price for bitcoin, but I'm thinking that a plan to secure the nation's finances with bitcoin-- similar to how other hard assets have been used throughout history-- might actually make sense.
I'm all in to returning those hard assets back to the people. If that's not realistic, use that money to finance public sectors, like healthcare or education, that the people have voted for. However, since the US government has historically held reserves in gold and other hard assets, with no desire to spend them in the present, it seems reasonable to consider converting those reserves into a stronger asset. That's all; no additional debt, just a practical acknowledgment of reality and a constructive alternative proposal.