The Federal Reserve isn't a single entity. Its composed of 12 different member Federal Reserve Banks. And The banks that are part of the Federal Reserve system own stock in the member Feds and have significant representation on it. Also blockchains are great if you care about transparency, immutability, and accessibility.
True. But its not programmable, in the way that Ethereum is for example. And that would be a nice feature to have in a payments system. PoW would never make sense for the Fed anyway - more likely PoS with some combination of Member Feds and participating FIs doing the staking and validating would make more sense.