I don't know of a single cryptocurrency or blockchain that doesn't also have intermediaries. Your transactions are still being verified by nodes on the network, and those nodes need to get paid with gas prices from your transaction outwise they just don't exist. Let's say the fed made their own node network assuming they aren't incompetent to not have some type of vulnerability in their protocol (they're not), and they make the usage free for citizens, they still have to pay for hardware, energy, administration, development, etc. If that transaction isn't levied by gas prices, it's just going to be a tax somewhere else. At which point it's still acting like a bank or clearing house in regards to fees and overhead.