When every transaction goes through FED, the government won't need to call or subpoena anyone to know where your money come and go.
They will be able do that, not for you, but to you.
And so much more.
The return address can be made up. Although the general area it is sent from is recorded in the form of zip code.
The contents of the letter are also not known.
So even if that info got out, there’s really not much information beyond the fact that mail was received, and we probably know who sent it.
Thats a world of difference from cryptographically signed transactions between known parties with known amounts.
Public enough that they can't play fast and loose like everyone else, but private where it matters in terms of not having literal Federally administered databases all just eafer for the reaping.
The Fed is fully governed by a federal agency. (The Fed Board of Governors).
The individual regional Fed banks are private-public hybrids, but they don't govern the system.