I would say this is a rather limited, technical understanding of a blockchain. The three most interesting aspects of a blockchain are (1) the state of blockchain is visible to all participants (2) the rules (the code) for changing the state is visible to all participants and (3) there is some mechanism to detect and punish rule breakers and aggressors who try to deform the state. Look at it this way and indeed a blockchain is really a very sophisticated collaboration model.
You don't need the distributed consensus or the decentralization or the trustlessness. There are blockchains with central coordinators and without trustlessness that may still prove very useful especially in global finance. People think Bitcoin or Ethereum are complicated but really, they are nothing compared to the global financial system. Distributed blockchain databases are much more elegant than what we have today in terms of achieving consensus on a very large (global) scale.
FedCoin is a crazy idea but it's not stupid. A national public ledger would open a lot of very interesting doors. (Though the republic would likely collapse, see my other comment.) Even if the Fed required only trusted nodes (ie bank-like entities) it still would provide everything from a true national ID system to real, binding peer-2-peer lending between citizens to a system where everybody has perfect, real-time visibility into the national economy (unlike the primitive system we have today where the Fed collects a bunch a data, massages it, and then announces it each month.) Lots of other problems -- everything from medical records to real-estate -- become a lot more tractable.